Scholars@Duke

• Background
• 

  Education, Training, & Certifications

  • Ph.D., University of California - Los Angeles 1990
  • M.S., Fudan University (China) 1985
  • B.S., Fudan University (China) 1982
• Recognition
• 

  In the News

  • APR 19, 2021

    Duke Research Blog

    The Physics of "In-Between" Is Changing Our Understanding of Physical Transitions

  • NOV 21, 2016

    Liu Named Fellow of the American Mathematical Society
• Expertise
• 

  Global Scholarship

  • Teaching

    • China (Country) 
• Research
• 

  Selected Grants

  • RTG: Training Tomorrow's Workforce in Analysis and Applications awarded by  National Science Foundation 2021 - 2026
  • Collaborative Research: Dynamics, singularities, and variational structure in models of fluids and clustering awarded by  National Science Foundation 2021 - 2024
  • Collaborative Research: Nonlocal models of aggregation and dispersion awarded by  National Science Foundation 2018 - 2021
  • Collaborative Research: Kinetic Models of Aggregation and Dispersion awarded by  National Science Foundation 2015 - 2019
  • Efficient Numerical Methods for Viscous Incompressible Flows awarded by  National Science Foundation 2009 - 2012
• Publications & Artistic Works
• 

  Selected Publications

  • Academic Articles

    • Lafata, Kyle J., Yushi Chang, Chunhao Wang, Yvonne M. Mowery, Irina Vergalasova, Donna Niedzwiecki, David S. Yoo, Jian-Guo Liu, David M. Brizel, and Fang-Fang Yin. “Intrinsic radiomic expression patterns after 20 Gy demonstrate early metabolic response of oropharyngeal cancers.” Med Phys 48, no. 7 (July 2021): 3767–77. https://doi.org/10.1002/mp.14926.
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    • Hu, J., J. G. Liu, Y. Xie, and Z. Zhou. “A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: Numerical analysis and exploration.” Journal of Computational Physics 433 (May 15, 2021). https://doi.org/10.1016/j.jcp.2021.110195.
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    • Gao, Y., and J. G. Liu. “Gradient flow formulation and second order numerical method for motion by mean curvature and contact line dynamics on rough surface.” Interfaces and Free Boundaries 23, no. 1 (January 1, 2021): 103–58. https://doi.org/10.4171/ifb/451.
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    • Li, Q., J. G. Liu, and R. Shu. “Sensitivity analysis of burgers' equation with shocks.” Siam Asa Journal on Uncertainty Quantification 8, no. 4 (January 1, 2021): 1493–1521. https://doi.org/10.1137/18M1211763.
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    • Gao, Yuan, Guangzhen Jin, and Jian-Guo Liu. “Inbetweening auto-animation via Fokker-Planck dynamics and thresholding.” Inverse Problems & Imaging 15, no. 5 (2021): 843–843. https://doi.org/10.3934/ipi.2021016.
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    • Liu, J. G., J. Wang, Y. Zhao, and Z. Zhou. “Field model for complex ionic fluids: Analytical properties and numerical investigation.” Communications in Computational Physics 30, no. 3 (January 1, 2021): 874–902. https://doi.org/10.4208/CICP.OA-2019-0223.
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    • Liu, J. G., and X. Xu. “Existence and incompressible limit of a tissue growth model with autophagy.” Siam Journal on Mathematical Analysis 53, no. 5 (January 1, 2021): 5215–42. https://doi.org/10.1137/21M1405253.
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    • Huang, H., J. G. Liu, and P. Pickl. “On the Mean-Field Limit for the Vlasov–Poisson–Fokker–Planck System.” Journal of Statistical Physics 181, no. 5 (December 1, 2020): 1915–65. https://doi.org/10.1007/s10955-020-02648-3.
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    • Gao, Y., J. G. Liu, J. Lu, and J. L. Marzuola. “Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects.” Nonlinearity 33, no. 8 (August 1, 2020): 3816–45. https://doi.org/10.1088/1361-6544/ab853d.
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    • Jin, S., L. Li, and J. G. Liu. “Convergence of the random batch method for interacting particles with disparate species and weights.” Siam Journal on Numerical Analysis 59, no. 2 (March 16, 2020): 746–68. https://doi.org/10.1137/20M1327641.
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    • Degond, P., M. Engel, J. G. Liu, and R. L. Pego. “A markov jump process modelling animal group size statistics.” Communications in Mathematical Sciences 18, no. 1 (January 1, 2020): 55–89. https://doi.org/10.4310/CMS.2020.v18.n1.a3.
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    • Feng, Y., T. Gao, L. Li, J. G. Liu, and Y. Lu. “Uniform-in-time weak error analysis for stochastic gradient descent algorithms via diffusion approximation.” Communications in Mathematical Sciences 18, no. 1 (January 1, 2020): 163–88. https://doi.org/10.4310/CMS.2020.v18.n1.a7.
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    • Gao, Y., J. G. Liu, T. Luo, and Y. Xiang. “Revisit of the peierls-nabarro model for edge dislocations in Hilbert space.” Discrete and Continuous Dynamical Systems  Series B 22, no. 11 (January 1, 2020). https://doi.org/10.3934/dcdsb.2020224.
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    • Gao, Yuan, and Jian-Guo Liu. “Long time behavior of dynamic solution to Peierls–Nabarro dislocation model.” Methods and Applications of Analysis 27, no. 2 (2020): 161–98. https://doi.org/10.4310/maa.2020.v27.n2.a4.
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    • Gao, Yuan, and Jian-Guo Liu. “A note on parametric Bayesian inference via gradient flows.” Annals of Mathematical Sciences and Applications 5, no. 2 (2020): 261–82. https://doi.org/10.4310/amsa.2020.v5.n2.a3.
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    • Jin, S., L. Li, and J. G. Liu. “Random Batch Methods (RBM) for interacting particle systems.” Journal of Computational Physics 400 (January 1, 2020). https://doi.org/10.1016/j.jcp.2019.108877.
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    • LIU, J. G., and J. WANG. “GLOBAL EXISTENCE FOR NERNST-PLANCK-NAVIER-STOKES SYSTEM IN R^N.” Communications in Mathematical Sciences 18, no. 6 (January 1, 2020): 1743–54. https://doi.org/10.4310/CMS.2020.v18.n6.a9.
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    • LIU, J. I. A. N. G. U. O., and X. XU. “A CLASS OF FUNCTIONAL INEQUALITIES AND THEIR APPLICATIONS TO FOURTH-ORDER NONLINEAR PARABOLIC EQUATIONS.” Communications in Mathematical Sciences 18, no. 7 (January 1, 2020): 1911–48. https://doi.org/10.4310/CMS.2020.V18.N7.A5.
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    • Li, L., Y. Li, J. G. Liu, Z. Liu, and J. Lu. “A stochastic version of stein variational gradient descent for efficient sampling.” Communications in Applied Mathematics and Computational Science 15, no. 1 (January 1, 2020): 37–63. https://doi.org/10.2140/camcos.2020.15.37.
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    • Li, L., and J. G. Liu. “Large time behaviors of upwind schemes and B-schemes for fokker-planck equations on R by jump processes.” Mathematics of Computation 89, no. 325 (January 1, 2020): 2283–2320. https://doi.org/10.1090/mcom/3516.
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    • Li, L., J. G. Liu, and P. Yu. “On the mean field limit for Brownian particles with Coulomb interaction in 3D.” Journal of Mathematical Physics 60, no. 11 (November 1, 2019). https://doi.org/10.1063/1.5114854.
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    • Liu, J. G., and R. L. Pego. “On Local Singularities in Ideal Potential Flows with Free Surface.” Chinese Annals of Mathematics. Series B 40, no. 6 (November 1, 2019): 925–48. https://doi.org/10.1007/s11401-019-0167-z.
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    • Liu, J. G., R. L. Pego, and Y. Pu. “Well-posedness and derivative blow-up for a dispersionless regularized shallow water system.” Nonlinearity 32, no. 11 (October 4, 2019): 4346–76. https://doi.org/10.1088/1361-6544/ab2cf1.
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    • Liu, J. G., R. L. Pego, and D. Slepčev. “Least action principles for incompressible flows and geodesics between shapes.” Calculus of Variations and Partial Differential Equations 58, no. 5 (October 1, 2019). https://doi.org/10.1007/s00526-019-1636-7.
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    • Lafata, Kyle J., Zhennan Zhou, Jian-Guo Liu, Julian Hong, Chris R. Kelsey, and Fang-Fang Yin. “An Exploratory Radiomics Approach to Quantifying Pulmonary Function in CT Images.” Sci Rep 9, no. 1 (August 8, 2019): 11509. https://doi.org/10.1038/s41598-019-48023-5.
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    • Liu, J. G., M. Tang, L. Wang, and Z. Zhou. “Analysis and computation of some tumor growth models with nutrient: From cell density models to free boundary dynamics.” Discrete and Continuous Dynamical Systems  Series B 24, no. 7 (July 1, 2019): 3011–35. https://doi.org/10.3934/dcdsb.2018297.
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    • Zhan, Q., M. Zhuang, Z. Zhou, J. G. Liu, and Q. H. Liu. “Complete-Q Model for Poro-Viscoelastic Media in Subsurface Sensing: Large-Scale Simulation with an Adaptive DG Algorithm.” Ieee Transactions on Geoscience and Remote Sensing 57, no. 7 (July 1, 2019): 4591–99. https://doi.org/10.1109/TGRS.2019.2891691.
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    • Liu, J. G., B. Niethammer, and R. L. Pego. “Self-similar Spreading in a Merging-Splitting Model of Animal Group Size.” Journal of Statistical Physics 175, no. 6 (June 30, 2019): 1311–30. https://doi.org/10.1007/s10955-019-02280-w.
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    • Liu, J. G., J. Lu, D. Margetis, and J. L. Marzuola. “Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model.” Physica D: Nonlinear Phenomena 393 (June 1, 2019): 54–67. https://doi.org/10.1016/j.physd.2019.01.004.
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    • Gao, Y., L. Li, and J. G. Liu. “Patched peakon weak solutions of the modified Camassa–Holm equation.” Physica D: Nonlinear Phenomena 390 (March 1, 2019): 15–35. https://doi.org/10.1016/j.physd.2018.10.005.
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    • Zhan, Qiwei, Mingwei Zhuang, Yuan Fang, Jian-Guo Liu, and Qing Huo Liu. “Green's function for anisotropic dispersive poroelastic media based on the Radon transform and eigenvector diagonalization.” Proceedings. Mathematical, Physical, and Engineering Sciences 475, no. 2221 (January 30, 2019): 20180610. https://doi.org/10.1098/rspa.2018.0610.
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    • Lafata, Kyle J., Julian C. Hong, Ruiqi Geng, Bradley G. Ackerson, Jian-Guo Liu, Zhennan Zhou, Jordan Torok, Chris R. Kelsey, and Fang-Fang Yin. “Association of pre-treatment radiomic features with lung cancer recurrence following stereotactic body radiation therapy.” Phys Med Biol 64, no. 2 (January 8, 2019): 025007. https://doi.org/10.1088/1361-6560/aaf5a5.
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    • De Hoop, M. V., J. G. Liu, P. A. Markowich, and N. S. Ussembayev. “Plane-wave analysis of a hyperbolic system of equations with relaxation in ℝ^d.” Communications in Mathematical Sciences 17, no. 1 (January 1, 2019): 61–79. https://doi.org/10.4310/cms.2019.v17.n1.a3.
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    • Gao, Y., J. G. Liu, and X. Y. Lu. “Gradient flow approach to an exponential thin film equation: Global existence and latent singularity.” Esaim  Control, Optimisation and Calculus of Variations 25 (January 1, 2019). https://doi.org/10.1051/cocv/2018037.
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    • Hu, Wenqing, Chris Junchi Li, Lei Li, and Jian-Guo Liu. “On the diffusion approximation of nonconvex stochastic gradient descent.” Annals of Mathematical Sciences and Applications 4, no. 1 (2019): 3–32. https://doi.org/10.4310/amsa.2019.v4.n1.a1.
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    • Huang, H., J. G. Liu, and J. Lu. “Learning interacting particle systems: Diffusion parameter estimation for aggregation equations.” Mathematical Models and Methods in Applied Sciences 29, no. 1 (January 1, 2019): 1–29. https://doi.org/10.1142/S0218202519500015.
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    • Lafata, K., Z. Zhou, J. G. Liu, and F. F. Yin. “Data clustering based on Langevin annealing with a self-consistent potential.” Quarterly of Applied Mathematics 77, no. 3 (January 1, 2019): 591–613. https://doi.org/10.1090/qam/1521.
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    • Li, L., and J. G. Liu. “A discretization of Caputo derivatives with application to time fractional SDEs and gradient flows.” Siam Journal on Numerical Analysis 57, no. 5 (January 1, 2019): 2095–2120. https://doi.org/10.1137/19M123854X.
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    • Liu, A., J. G. Liu, and Y. Lu. “On the rate of convergence of empirical measure in ∞-Wasserstein distance for unbounded density function.” Quarterly of Applied Mathematics 77, no. 4 (January 1, 2019): 811–29. https://doi.org/10.1090/qam/1541.
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    • Liu, J. G., and R. M. Strain. “Global stability for solutions to the exponential PDE describing epitaxial growth.” Interfaces and Free Boundaries 21, no. 1 (January 1, 2019): 61–86. https://doi.org/10.4171/IFB/417.
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    • Gao, Y., H. Ji, J. G. Liu, and T. P. Witelski. “A vicinal surface model for epitaxial growth with logarithmic free energy.” Discrete and Continuous Dynamical Systems  Series B 23, no. 10 (December 1, 2018): 4433–53. https://doi.org/10.3934/dcdsb.2018170.
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    • Feng, Y., L. Li, J. G. Liu, and X. Xu. “Continuous and discrete one dimensional autonomous fractional odes.” Discrete and Continuous Dynamical Systems  Series B 23, no. 8 (October 1, 2018): 3109–35. https://doi.org/10.3934/dcdsb.2017210.
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    • Feng, Y., L. Li, J. G. Liu, and X. Xu. “A note on one-dimensional time fractional ODEs.” Applied Mathematics Letters 83 (September 1, 2018): 87–94. https://doi.org/10.1016/j.aml.2018.03.015.
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    • Li, L., J. G. Liu, and L. Wang. “Cauchy problems for Keller–Segel type time–space fractional diffusion equation.” Journal of Differential Equations 265, no. 3 (August 5, 2018): 1044–96. https://doi.org/10.1016/j.jde.2018.03.025.
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    • Gao, Y., and J. G. Liu. “The modified camassa-holm equation in lagrangian coordinates.” Discrete and Continuous Dynamical Systems  Series B 23, no. 6 (August 1, 2018): 2545–92. https://doi.org/10.3934/dcdsb.2018067.
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    • Liu, J. G., M. Tang, L. Wang, and Z. Zhou. “An accurate front capturing scheme for tumor growth models with a free boundary limit.” Journal of Computational Physics 364 (July 1, 2018): 73–94. https://doi.org/10.1016/j.jcp.2018.03.013.
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    • Chen, K., Q. Li, and J. G. Liu. “Online learning in optical tomography: A stochastic approach.” Inverse Problems 34, no. 7 (May 29, 2018). https://doi.org/10.1088/1361-6420/aac220.
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    • Liu, J. G., and X. Xu. “Partial regularity of weak solutions to a PDE system with cubic nonlinearity.” Journal of Differential Equations 264, no. 8 (April 15, 2018): 5489–5526. https://doi.org/10.1016/j.jde.2018.01.001.
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    • Li, L., and J. G. Liu. “p-Euler equations and p-Navier–Stokes equations.” Journal of Differential Equations 264, no. 7 (April 5, 2018): 4707–48. https://doi.org/10.1016/j.jde.2017.12.023.
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    • Gao, Y., J. G. Liu, X. Y. Lu, and X. Xu. “Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface.” Calculus of Variations and Partial Differential Equations 57, no. 2 (April 1, 2018). https://doi.org/10.1007/s00526-018-1326-x.
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    • Coquel, F., S. Jin, J. G. Liu, and L. Wang. “Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and glimm front sampling for scalar conservation laws.” Mathematics of Computation 87, no. 311 (January 1, 2018): 1083–1126. https://doi.org/10.1090/mcom/3253.
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    • Feng, Y., L. Li, and J. G. Liu. “Semigroups of stochastic gradient descent and online principal component analysis: Properties and diffusion approximations.” Communications in Mathematical Sciences 16, no. 3 (January 1, 2018): 777–89. https://doi.org/10.4310/cms.2018.v16.n3.a8.
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    • Gao, Y., L. Li, and J. G. Liu. “A dispersive regularization for the modified camassa–holm equation.” Siam Journal on Mathematical Analysis 50, no. 3 (January 1, 2018): 2807–38. https://doi.org/10.1137/17M1132756.
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    • Li, L., and J. G. Liu. “A note on deconvolution with completely monotone sequences and discrete fractional calculus.” Quarterly of Applied Mathematics 76, no. 1 (January 1, 2018): 189–98. https://doi.org/10.1090/qam/1479.
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    • Li, L., and J. G. Liu. “A generalized definition of caputo derivatives and its application to fractional odes.” Siam Journal on Mathematical Analysis 50, no. 3 (January 1, 2018): 2867–2900. https://doi.org/10.1137/17M1160318.
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    • Li, L., and J. G. Liu. “Some compactness criteria for weak solutions of time fractional pdes.” Siam Journal on Mathematical Analysis 50, no. 4 (January 1, 2018): 3963–95. https://doi.org/10.1137/17M1145549.
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    • Liu, J. G., L. Wang, and Z. Zhou. “Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations.” Mathematics of Computation 87, no. 311 (January 1, 2018): 1165–89. https://doi.org/10.1090/mcom/3250.
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    • Jin, Shi, Jian-Guo Liu, and Zheng Ma. “Uniform spectral convergence of the stochastic Galerkin method for the linear transport equations with random inputs in diffusive regime and a micro–macro decomposition-based asymptotic-preserving method.” Research in the Mathematical Sciences 4, no. 1 (December 2017). https://doi.org/10.1186/s40687-017-0105-1.
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    • Li, L., J. G. Liu, and J. Lu. “Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem.” Journal of Statistical Physics 169, no. 2 (October 1, 2017): 316–39. https://doi.org/10.1007/s10955-017-1866-z.
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    • Gao, Y., H. Ji, J. G. Liu, and T. P. Witelski. “Global existence of solutions to a tear film model with locally elevated evaporation rates.” Physica D: Nonlinear Phenomena 350 (July 1, 2017): 13–25. https://doi.org/10.1016/j.physd.2017.03.005.
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    • Liu, J. G., Z. Ma, and Z. Zhou. “Explicit and Implicit TVD Schemes for Conservation Laws with Caputo Derivatives.” Journal of Scientific Computing 72, no. 1 (July 1, 2017): 291–313. https://doi.org/10.1007/s10915-017-0356-4.
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    • Gao, Y., J. G. Liu, and J. Lu. “Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces.” Journal of Nonlinear Science 27, no. 3 (June 1, 2017): 873–926. https://doi.org/10.1007/s00332-016-9354-1.
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    • Liu, J. G., and J. Wang. “Global existence for a thin film equation with subcritical mass.” Discrete and Continuous Dynamical Systems  Series B 22, no. 4 (June 1, 2017): 1461–92. https://doi.org/10.3934/dcdsb.2017070.
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    • Degond, P., J. G. Liu, and R. L. Pego. “Coagulation–Fragmentation Model for Animal Group-Size Statistics.” Journal of Nonlinear Science 27, no. 2 (April 1, 2017): 379–424. https://doi.org/10.1007/s00332-016-9336-3.
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    • Cong, W., and J. G. Liu. “Uniform L^∞ boundedness for a degenerate parabolic-parabolic Keller-Segel model.” Discrete and Continuous Dynamical Systems  Series B 22, no. 2 (March 1, 2017): 307–38. https://doi.org/10.3934/dcdsb.2017015.
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    • Degond, P., J. G. Liu, S. Merino-Aceituno, and T. Tardiveau. “Continuum dynamics of the intention field under weakly cohesive social interaction.” Mathematical Models and Methods in Applied Sciences 27, no. 1 (January 1, 2017): 159–82. https://doi.org/10.1142/S021820251740005X.
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    • Degond, P., M. Herty, and J. G. Liu. “Meanfield games and model predictive control.” Communications in Mathematical Sciences 15, no. 5 (January 1, 2017): 1403–22. https://doi.org/10.4310/CMS.2017.v15.n5.a9.
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    • Gao, Y., J. G. Liu, and J. Lu. “Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime.” Siam Journal on Mathematical Analysis 49, no. 3 (January 1, 2017): 1705–31. https://doi.org/10.1137/16M1094543.
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    • Gao, Y., and J. G. Liu. “Global convergence of a sticky particle method for the modified Camassa-Holm equation.” Siam Journal on Mathematical Analysis 49, no. 2 (January 1, 2017): 1267–94. https://doi.org/10.1137/16M1102069.
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    • Huang, H., and J. G. Liu. “Error estimate of a random particle blob method for the Keller-Segel equation.” Mathematics of Computation 86, no. 308 (January 1, 2017): 2719–44. https://doi.org/10.1090/mcom/3174.
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    • Huang, H., and J. G. Liu. “Discrete-in-time random particle blob method for the Keller-Segel equation and convergence analysis.” Communications in Mathematical Sciences 15, no. 7 (January 1, 2017): 1821–42. https://doi.org/10.4310/CMS.2017.v15.n7.a2.
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    • Liu, J. G., and J. Wang. “A generalized Sz. Nagy inequality in higher dimensions and the critical thin film equation.” Nonlinearity 30, no. 1 (January 1, 2017): 35–60. https://doi.org/10.1088/0951-7715/30/1/35.
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    • Liu, J. G., and R. Yang. “A random particle blob method for the keller-segel equation and convergence analysis.” Mathematics of Computation 86, no. 304 (January 1, 2017): 725–45. https://doi.org/10.1090/mcom/3118.
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    • Liu, J. G., and X. Xu. “Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions.” Siam Journal on Mathematical Analysis 49, no. 3 (January 1, 2017): 2220–45. https://doi.org/10.1137/16M1098474.
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    • Huang, H., and J. G. Liu. “Error estimates of the aggregation-diffusion splitting algorithms for the Keller-Segel equations.” Discrete and Continuous Dynamical Systems  Series B 21, no. 10 (December 1, 2016): 3463–78. https://doi.org/10.3934/dcdsb.2016107.
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    • Liu, Jian-Guo, and Rong Yang. “Propagation of chaos for large Brownian particle system with Coulomb interaction.” Research in the Mathematical Sciences 3, no. 1 (December 2016). https://doi.org/10.1186/s40687-016-0086-5.
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    • Huang, H., and J. G. Liu. “A note on Monge-Ampère Keller-Segel equation.” Applied Mathematics Letters 61 (November 1, 2016): 26–34. https://doi.org/10.1016/j.aml.2016.05.003.
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    • Herschlag, G., J. G. Liu, and A. T. Layton. “Fluid extraction across pumping and permeable walls in the viscous limit.” Physics of Fluids 28, no. 4 (April 1, 2016). https://doi.org/10.1063/1.4946005.
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    • Liu, J. G., and J. Wang. “A Note on L∞-Bound and Uniqueness to a Degenerate Keller-Segel Model.” Acta Applicandae Mathematicae 142, no. 1 (April 1, 2016): 173–88. https://doi.org/10.1007/s10440-015-0022-5.
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    • Liu, Jian-Guo, and Jinhuan Wang. “Refined hyper-contractivity and uniqueness for the Keller–Segel equations.” Applied Mathematics Letters 52 (February 2016): 212–19. https://doi.org/10.1016/j.aml.2015.09.001.
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    • Chen, J., J. G. Liu, and Z. Zhou. “On a Schrödinger-Landau-Lifshitz system: Variational structure and numerical methods.” Multiscale Modeling and Simulation 14, no. 4 (January 1, 2016): 1463–87. https://doi.org/10.1137/16M106947X.
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    • Cong, W., and J. G. Liu. “A degenerate p-laplacian keller-segel model.” Kinetic and Related Models 9, no. 4 (January 1, 2016): 687–714. https://doi.org/10.3934/krm.2016012.
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    • Huang, H., and J. G. Liu. “Well-posedness for the keller-segel equation with fractional laplacian and the theory of propagation of chaos.” Kinetic and Related Models 9, no. 4 (January 1, 2016): 715–48. https://doi.org/10.3934/krm.2016013.
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    • Liu, J. G., and R. L. Pego. “On generating functions of hausdorff moment sequences.” Transactions of the American Mathematical Society 368, no. 12 (January 1, 2016): 8499–8518. https://doi.org/10.1090/tran/6618.
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    • Liu, J. G., and X. Xu. “Existence theorems for a multidimensional crystal surface model.” Siam Journal on Mathematical Analysis 48, no. 6 (January 1, 2016): 3667–87. https://doi.org/10.1137/16M1059400.
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    • Degond, P., A. Frouvelle, and J. G. Liu. “Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics.” Archive for Rational Mechanics and Analysis 216, no. 1 (April 1, 2015): 63–115. https://doi.org/10.1007/s00205-014-0800-7.
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    • Xue, Y., C. Wang, and J. G. Liu. “Simple Finite Element Numerical Simulation of Incompressible Flow Over Non-rectangular Domains and the Super-Convergence Analysis.” Journal of Scientific Computing 65, no. 3 (March 14, 2015): 1189–1216. https://doi.org/10.1007/s10915-015-0005-8.
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    • Lu, J., J. G. Liu, and D. Margetis. “Emergence of step flow from an atomistic scheme of epitaxial growth in 1+1 dimensions.” Physical Review E  Statistical, Nonlinear, and Soft Matter Physics 91, no. 3 (March 4, 2015). https://doi.org/10.1103/PhysRevE.91.032403.
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    • Chertock, A., J. G. Liu, and T. Pendleton. “Elastic collisions among peakon solutions for the Camassa-Holm equation.” Applied Numerical Mathematics 93 (January 1, 2015): 30–46. https://doi.org/10.1016/j.apnum.2014.01.001.
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    • Herschlag, G., J. G. Liu, and A. T. Layton. “An exact solution for stokes flow in a channel with arbitrarily large wall permeability.” Siam Journal on Applied Mathematics 75, no. 5 (January 1, 2015): 2246–67. https://doi.org/10.1137/140995854.
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    • Degond, Pierre, Jian-Guo Liu, and Christian Ringhofer. “Evolution of wealth in a non-conservative economy driven by local Nash equilibria.” Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences 372, no. 2028 (November 2014). https://doi.org/10.1098/rsta.2013.0394.
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    • Johnston, H., C. Wang, and J. G. Liu. “A Local Pressure Boundary Condition Spectral Collocation Scheme for the Three-Dimensional Navier–Stokes Equations.” Journal of Scientific Computing 60, no. 3 (September 1, 2014): 612–26. https://doi.org/10.1007/s10915-013-9808-7.
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    • Goudon, T., S. Jin, J. G. Liu, and B. Yan. “Asymptotic-preserving schemes for kinetic-fluid modeling of disperse two-phase flows with variable fluid density.” International Journal for Numerical Methods in Fluids 75, no. 2 (May 20, 2014): 81–102. https://doi.org/10.1002/fld.3885.
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    • Duan, Y., and J. G. Liu. “Convergence analysis of the vortex blob method for the b-equation.” Discrete and Continuous Dynamical Systems  Series A 34, no. 5 (May 1, 2014): 1995–2011. https://doi.org/10.3934/dcds.2014.34.1995.
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    • Bian, S., J. G. Liu, and C. Zou. “Ultra-contractivity for keller-segel model with diffusion exponent m > 1-2/d.” Kinetic and Related Models 7, no. 1 (March 1, 2014): 9–28. https://doi.org/10.3934/krm.2014.7.9.
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    • Degond, P., J. G. Liu, and C. Ringhofer. “Evolution of the Distribution of Wealth in an Economic Environment Driven by Local Nash Equilibria.” Journal of Statistical Physics 154, no. 3 (February 1, 2014): 751–80. https://doi.org/10.1007/s10955-013-0888-4.
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    • Chae, D., P. Degond, and J. G. Liu. “Well-posedness for hall-magnetohydrodynamics.” Annales De L’Institut Henri Poincare (C) Analyse Non Lineaire 31, no. 3 (January 1, 2014): 555–65. https://doi.org/10.1016/j.anihpc.2013.04.006.
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    • Chen, X., A. Jüngel, and J. G. Liu. “A note on Aubin-Lions-Dubinskiǐ Lemmas.” Acta Applicandae Mathematicae 133, no. 1 (January 1, 2014): 33–43. https://doi.org/10.1007/s10440-013-9858-8.
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    • Chen, X., X. Li, and J. G. Liu. “Existence and uniqueness of global weak solution to a kinetic model for the sedimentation of rod-like particles.” Communications in Mathematical Sciences 12, no. 8 (January 1, 2014): 1579–1601. https://doi.org/10.4310/CMS.2014.v12.n8.a10.
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    • Coquel, F., S. Jin, J. G. Liu, and L. Wang. “Well-Posedness and Singular Limit of a Semilinear Hyperbolic Relaxation System with a Two-Scale Discontinuous Relaxation Rate.” Archive for Rational Mechanics and Analysis 214, no. 3 (January 1, 2014): 1051–84. https://doi.org/10.1007/s00205-014-0773-6.
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    • Degond, P., J. G. Liu, and C. Ringhofer. “Large-scale dynamics of mean-field games driven by local nash equilibria.” Journal of Nonlinear Science 24, no. 1 (January 1, 2014): 93–115. https://doi.org/10.1007/s00332-013-9185-2.
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    • Degond, P., M. Herty, and J. G. Liu. “Flow on sweeping networks.” Multiscale Modeling and Simulation 12, no. 2 (January 1, 2014): 538–65. https://doi.org/10.1137/130927061.
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    • Goudon, T., S. Jin, J. -. G. Liu, and B. Yan. “Asymptotic-preserving schemes for kinetic-fluid modeling of disperse two-phase flows with variable fluid density.” International Journal for Numerical Methods in Fluids, 2014.
    • Huang, Y. L., J. G. Liu, and W. C. Wang. “A generalized mac scheme on curvilinear domains.” Siam Journal on Scientific Computing 35, no. 5 (November 7, 2013). https://doi.org/10.1137/120875508.
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    • Bian, S., and J. G. Liu. “Dynamic and Steady States for Multi-Dimensional Keller-Segel Model with Diffusion Exponent m > 0.” Communications in Mathematical Physics 323, no. 3 (November 1, 2013): 1017–70. https://doi.org/10.1007/s00220-013-1777-z.
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    • Chen, X., and J. G. Liu. “Analysis of polymeric flow models and related compactness theorems in weighted spaces.” Siam Journal on Mathematical Analysis 45, no. 3 (October 4, 2013): 1179–1215. https://doi.org/10.1137/120887850.
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    • Goudon, T., S. Jin, J. G. Liu, and B. Yan. “Asymptotic-preserving schemes for kinetic-fluid modeling of disperse two-phase flows.” Journal of Computational Physics 246 (August 1, 2013): 145–64. https://doi.org/10.1016/j.jcp.2013.03.038.
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    • Degond, P., A. Frouvelle, and J. G. Liu. “Macroscopic limits and phase transition in a system of self-propelled particles.” Journal of Nonlinear Science 23, no. 3 (June 1, 2013): 427–56. https://doi.org/10.1007/s00332-012-9157-y.
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    • Chen, X., and J. G. Liu. “Global weak entropy solution to Doi-Saintillan-Shelley model for active and passive rod-like and ellipsoidal particle suspensions.” Journal of Differential Equations 254, no. 7 (April 1, 2013): 2764–2802. https://doi.org/10.1016/j.jde.2013.01.005.
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    • Chae, D., P. Degond, and J. -. G. Liu. “Well-posedness for Hall-magnetohydrodynamics.” Annales De L’Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis, 2013.
    • Chen, X., A. Jüngel, and J. -. G. Liu. “A Note on Aubin-Lions-Dubinskiǐ Lemmas.” Acta Applicandae Mathematicae, 2013, 1–11.
    • Degond, P., J. -. G. Liu, and C. Ringhofer. “Evolution of the Distribution of Wealth in an Economic Environment Driven by Local Nash Equilibria.” Journal of Statistical Physics, 2013, 1–30.
    • Degond, P., J. -. G. Liu, and C. Ringhofer. “Large-Scale Dynamics of Mean-Field Games Driven by Local Nash Equilibria.” Journal of Nonlinear Science, 2013, 1–23.
    • Degond, P., and J. G. Liu. “Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation.” Mathematical Models and Methods in Applied Sciences 22, no. SUPPL.1 (April 1, 2012). https://doi.org/10.1142/S021820251140001X.
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    • Carrillo, J., L. Chen, J. G. Liu, and J. Wang. “A note on the subcritical two dimensional Keller-Segel system.” Acta Applicanda Mathematicae 119 (2012): 43–55.
    • Chen, L., J. G. Liu, and J. Wang. “Multi-dimensional degenerate Keller-Segel system with critical diffusion exponent 2n/(n+2).” Siam J. Math Anal 44 (2012): 1077–1102.
    • Chen, X., and J. G. Liu. “Two nonlinear compactness theorems in L^p(0,T;B).” Applied Mathematics Letters 25, no. 12 (January 1, 2012): 2252–57. https://doi.org/10.1016/j.aml.2012.06.012.
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    • Chertock, A., J. G. Liu, and T. Pendleton. “Convergence of a particle method and global weak solutions of a family of evolutionary PDEs.” Siam J. Numer. Anal. 50 (2012): 1–21.
    • Frouvelle, A., and J. G. Liu. “Dynamics in a kinetic model of oriented particles with phase transition.” Siam J. Math Anal 44 (2012): 791–826.
    • Haack, J., S. Jin, and J. G. Liu. “An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equations.” Commun. Comput. Phy. 12 (2012): 955–80.
    • Chae, D., and J. G. Liu. “Blow-up, zero alpha limit and the Liouville type theorem for the Euler-Poincare equations.” Comm. Math. Phy., 314 (2012): 671–87.
    • Zheng, W., H. Gao, J. G. Liu, Y. Zhang, Q. Ye, and C. Swank. “General solution to gradient-induced transverse and longitudinal relaxation of spins undergoing restricted diffusion.” Physical Review a  Atomic, Molecular, and Optical Physics 84, no. 5 (November 14, 2011). https://doi.org/10.1103/PhysRevA.84.053411.
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    • Acheritogaray, M., P. Degond, A. Frouvelle, and J. G. Liu. “Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system.” Kinetic and Related Models 4 (2011): 901–18.
    • Huang, Y. L., J. G. Liu, and W. C. Wang. “An FFT based fast poisson solver on spherical shells.” Communications in Computational Physics 9, no. 3 (January 1, 2011): 649–67. https://doi.org/10.4208/cicp.060509.080609s.
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    • Liu, J. G., and A. Lorz. “A coupled chemotaxis-fluid model: Global existence.” Ann. I. H. Poincare, An 28 (2011): 643–52.
    • Jin, S., J. G. Liu, and L. Wang. “A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations (Accepted).” Math. Comp., 2011.
    • Liu, J. G., J. Liu, and R. L. Pego. “Stable and accurate pressure approximation for unsteady incompressible viscous flow.” Journal of Computational Physics 229, no. 9 (January 1, 2010): 3428–53. https://doi.org/10.1016/j.jcp.2010.01.010.
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    • Liu, J. G., and L. Mieussens. “Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit.” Siam J. Numer. Anal. 48 (2010): 1474–91.
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    • Liu, J. G., and R. L. Pego. “Stable discretization of magnetohydrodynamics in bounded domains.” Communications in Mathematical Sciences 8, no. 1 (January 1, 2010): 235–51. https://doi.org/10.4310/CMS.2010.v8.n1.a12.
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    • Liu, J. G., and R. Pego. “Stable discretization of magnetohydrodynamics in bounded domains.” Commun. Math. Sci. 8 (2010): 234–51.
    • Liu, J. G., J. Liu, and R. L. Pego. “Error estimates for finite-element Navier-Stokes solvers without standard Inf-Sup conditions.” Chinese Annals of Mathematics. Series B 30, no. 6 (December 1, 2009): 743–68. https://doi.org/10.1007/s11401-009-0116-3.
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    • Liu, J. G., and W. C. Wang. “Characterization and regularity for axisymmetric solenoidal vector fields with application to navier-stokes equation.” Siam Journal on Mathematical Analysis 41, no. 5 (December 1, 2009): 1825–50. https://doi.org/10.1137/080739744.
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    • Ha, S. Y., and J. G. Liu. “A simple proof of the Cucker-Smale flocking dynamics and mean-field limit.” Commun. Math. Sci. 7 (2009): 297–325.
    • Degond, P., J. G. Liu, and M. H. Vignal. “Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit.” Siam Journal on Numerical Analysis 46, no. 3 (November 10, 2008): 1298–1322. https://doi.org/10.1137/070690584.
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    • Lin, P., J. G. Liu, and X. Lu. “Long time numerical solution of the Navier-Stokes equations based on a sequential regularization formulation.” Siam Journal on Scientific Computing 31, no. 1 (November 5, 2008): 398–419. https://doi.org/10.1137/060673722.
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    • Lu, X., P. Lin, and J. G. Liu. “Analysis of a sequential regularization method for the unsteady Navier-Stokes equations.” Mathematics of Computation 77, no. 263 (July 1, 2008): 1467–94. https://doi.org/10.1090/S0025-5718-08-02087-5.
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    • Hsia, C. H., J. G. Liu, and C. Wang. “Structural stability and bifurcation for 2D incompressible ows with symmetry.” Meth. Appl. Anal. 15 (2008): 495–512.
    • Liu, J. G., and C. Wang. “A fourth order numerical method for the primtive equations formulated in mean vorticity.” Communications in Computational Physics 4, no. 1 (January 1, 2008): 26–55.
    • Antman, S. S., and J. G. Liu. “Basic themes and pretty problems of nonlinear solid mechanics.” Milan Journal of Mathematics 75, no. 1 (December 1, 2007): 135–76. https://doi.org/10.1007/s00032-007-0068-6.
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    • Moore, Jeffrey, Zhihong Cheng, Junjie Hao, Gang Guo, Jian-Guo Liu, Chunjian Lin, and Liangli Lucy Yu. “Effects of solid-state yeast treatment on the antioxidant properties and protein and fiber compositions of common hard wheat bran.” Journal of Agricultural and Food Chemistry 55, no. 25 (December 2007): 10173–82. https://doi.org/10.1021/jf071590o.
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    • Liu, J. G., J. Liu, and R. L. Pego. “Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate.” Communications on Pure and Applied Mathematics 60, no. 10 (October 1, 2007): 1443–87. https://doi.org/10.1002/cpa.20178.
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    • Degond, P., S. Jin, and J. G. Liu. “Mach-number uniform asymptotic- preserving Gauge schemes for compressible flows.” Bulletin of the Institute of Mathematics Academia Sinica (New Series) 2 (2007): 851–92.
    • Liu, J. G., J. Liu, and R. Pego. “Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate via a commutator estimate.” Comm. Pure Appl. Math. 60 (2007): 1443–87.
    • Liu, J. G., and W. C. Wang. “Convergence analysis of the energy and helicity preserving scheme for axisymmetric flows.” Siam Journal on Numerical Analysis 44, no. 6 (December 1, 2006): 2456–80. https://doi.org/10.1137/050639314.
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    • Degond, P., J. G. Liu, and L. Mieussens. “Macroscopic fluid models with localized kinetic upscaling effects.” Multiscale Modeling and Simulation 5, no. 3 (September 1, 2006): 940–79. https://doi.org/10.1137/060651574.
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    • Moore, Jeffrey, Jian-Guo Liu, Kequan Zhou, and Liangli Lucy Yu. “Effects of genotype and environment on the antioxidant properties of hard winter wheat bran.” Journal of Agricultural and Food Chemistry 54, no. 15 (July 2006): 5313–22. https://doi.org/10.1021/jf060381l.
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    • Liu, J. G., R. Samelson, and C. Wang. “Global weak solution of planetary geostrophic equations with inviscid geostrophic balance.” International Journal of Phytoremediation 85, no. 6–7 (January 1, 2006): 593–605. https://doi.org/10.1080/00036810500328299.
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    • Liu, J. G., and W. C. Wang. “Energy and helicity preserving schemes for hydro- and magnetohydro-dynamics flows with symmetry.” Journal of Computational Physics 200, no. 1 (October 10, 2004): 8–33. https://doi.org/10.1016/j.jcp.2004.03.005.
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    • Ghil, M., J. G. Liu, C. Wang, and S. Wang. “Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow.” Physica D: Nonlinear Phenomena 197, no. 1–2 (October 1, 2004): 149–73. https://doi.org/10.1016/j.physd.2004.06.012.
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    • Li, B., and J. G. Liu. “Epitaxial growth without slope selection: Energetics, coarsening, and dynamic scaling.” Journal of Nonlinear Science 14, no. 5 (October 1, 2004): 429–51. https://doi.org/10.1007/s00332-004-0634-9.
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    • Johnston, H., and J. G. Liu. “Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term.” Journal of Computational Physics 199, no. 1 (September 1, 2004): 221–59. https://doi.org/10.1016/j.jcp.2004.02.009.
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    • Wang, C., J. G. Liu, and H. Johnston. “Analysis of a fourth order finite difference method for the incompressible Boussinesq equations.” Numerische Mathematik 97, no. 3 (May 1, 2004): 555–94. https://doi.org/10.1007/s00211-003-0508-3.
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    • Li, B., and J. G. Liu. “Eptaxial growth without slope selection: energetics, coarsening, and dynamic scaling.” J. Nonlinear Sci. 14 (2004): 429–51.
    • Lin, H. E., J. G. Liu, and W. Q. Xu. “Effects of small viscosity and far field boundary conditions for hyperbolic systems.” Communications on Pure and Applied Analysis 3, no. 2 (January 1, 2004): 267–90. https://doi.org/10.3934/cpaa.2004.3.267.
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    • Liu, J. G., and C. Wang. “High order finite difference method for unsteady incompressible flow on multi-connected domain in vorticity-stream function formulation.” Computer and Fluids 33 (2004): 223–55.
    • Liu, J. G., and C. Wang. “High order finite difference methods for unsteady incompressible flows in multi-connected domains.” Computers and Fluids 33, no. 2 (January 1, 2004): 223–55. https://doi.org/10.1016/S0045-7930(03)00037-9.
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    • Liu, J. G., and W. Q. Xu. “Far field boundary condition for convection diffusion equation at zero viscosity limit.” Quarterly of Applied Mathematics 62, no. 1 (January 1, 2004): 27–52. https://doi.org/10.1090/qam/2032571.
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    • Duraisamy, K., J. D. Baeder, and J. G. Liu. “Concepts and Application of Time-Limiters to High Resolution Schemes.” Journal of Scientific Computing 19, no. 1–3 (December 1, 2003): 139–62. https://doi.org/10.1023/A:1025395707090.
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    • Li, B., and J. G. Liu. “Thin film epitaxy with or without slope selection.” European Journal of Applied Mathematics 14, no. 6 (December 1, 2003): 713–43. https://doi.org/10.1017/S095679250300528X.
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    • Liu, J. G., C. Wang, and H. Johnston. “A Fourth Order Scheme for Incompressible Boussinesq Equations.” Journal of Scientific Computing 18, no. 2 (April 1, 2003): 253–85. https://doi.org/10.1023/A:1021168924020.
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    • Chainais-Hillairet, C., J. G. Liu, and Y. J. Peng. “Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis.” Mathematical Modelling and Numerical Analysis 37, no. 2 (January 1, 2003): 319–38. https://doi.org/10.1051/m2an:2003028.
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    • Chern, I. L., J. G. Liu, and W. C. Wang. “Accurate evaluation of electrostatics for macromolecules in solution.” Methods and Applications of Analysis 10 (2003): 309–28.
    • Wang, C., and J. G. Liu. “Positivity property of second-order flux-splitting schemes for the compressible Euler equations.” Discrete and Continuous Dynamical Systems  Series B 3, no. 2 (January 1, 2003): 201–28. https://doi.org/10.3934/dcdsb.2003.3.201.
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    • Wang, C., and J. G. Liu. “Fourth order convergence of a compact difference solver for incompressible flow.” Commun. Appl. Anal. 7 (2003): 171–91.
    • Weinan, E., and J. G. Liu. “Gauge method for viscous incompressible flows.” Comm. Math. Sci. 1 (2003): 317–32.
    • Johnston, H., and J. G. Liu. “Finite difference schemes for incompressible flow based on local pressure boundary conditions.” Journal of Computational Physics 180, no. 1 (July 20, 2002): 120–54. https://doi.org/10.1006/jcph.2002.7079.
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    • Wang, C., and J. G. Liu. “Analysis of finite difference schemes for unsteady Navier-Stokes equations in vorticity formulation.” Numerische Mathematik 91, no. 3 (May 1, 2002): 543–76. https://doi.org/10.1007/s002110100311.
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    • Weinan, E., and J. G. Liu. “Projection method III: Spatial discretization on the staggered grid.” Mathematics of Computation 71, no. 237 (January 1, 2002): 27–47. https://doi.org/10.1090/S0025-5718-01-01313-8.
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    • Liu, J. G., and W. C. Wang. “An energy-preserving MAC-Yee scheme for the incompressible MHD equation.” Journal of Computational Physics 174, no. 1 (November 20, 2001): 12–37. https://doi.org/10.1006/jcph.2001.6772.
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    • Liu, J. G., and E. Weinan. “Simple finite element method in vorticity formulation for incompressible flows.” Mathematics of Computation 70, no. 234 (April 1, 2001): 579–93. https://doi.org/10.1090/S0025-5718-00-01239-4.
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    • Liu, J. G., and Z. Xin. “Convergence of the point vortex method for 2-D vortex sheet.” Mathematics of Computation 70, no. 234 (April 1, 2001): 595–606. https://doi.org/10.1090/S0025-5718-00-01271-0.
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    • Liu, J. G., and E. Weinan. “Simple finite element method in vorticity formulation for incompressible flow.” Math. Comp. 69 (2001): 1385–1407.
    • Liu, J. G., and Z. Xin. “Convergence of point vortex method for 2-D vortex sheet.” Math. Comp. 70 (2001): 565–606.
    • Weinan, E., and J. G. Liu. “Gauge finite element method for incompressible flows.” International Journal for Numerical Methods in Fluids 34, no. 8 (December 1, 2000): 701–10. https://doi.org/10.1002/1097-0363(20001230)34:8<701::AID-FLD76>3.0.CO;2-B.
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    • Liu, J. G., and Z. P. Xin. “Convergence of a Galerkin method for 2-D discontinuous Euler flows.” Communications on Pure and Applied Mathematics 53, no. 6 (June 1, 2000): 786–98. https://doi.org/10.1002/(SICI)1097-0312(200006)53:6<786::AID-CPA3>3.3.CO;2-P.
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    • Liu, J. G., and C. W. Shu. “A High-Order Discontinuous Galerkin Method for 2D Incompressible Flows.” Journal of Computational Physics 160, no. 2 (May 20, 2000): 577–96. https://doi.org/10.1006/jcph.2000.6475.
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    • Liu, J. G., and Z. Xin. “Convergence of a Galerkin method for 2-D discontinuous Euler flows.” Communications on Pure and Applied Mathematics 53, no. 6 (January 1, 2000): 786–98. https://doi.org/10.1002/(SICI)1097-0312(200006)53:6<786::AID-CPA3>3.0.CO;2-Y.
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    • Wang, C., and J. G. Liu. “Convergence of gauge method for incompressible flow.” Mathematics of Computation 69, no. 232 (January 1, 2000): 1385–1407. https://doi.org/10.1090/s0025-5718-00-01248-5.
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    • Lefloch, P. G., and J. G. Liu. “Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions.” Mathematics of Computation 68, no. 227 (January 1, 1999): 1025–55. https://doi.org/10.1090/s0025-5718-99-01062-5.
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    • Wang, Z. J., J. G. Liu, and S. Childress. “Connection between corner vortices and shear layer instability in flow past an ellipse.” Physics of Fluids 11, no. 9 (January 1, 1999): 2446–48. https://doi.org/10.1063/1.870108.
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    • Choi, H., and J. G. Liu. “The Reconstruction of Upwind Fluxes for Conservation Laws: Its Behavior in Dynamic and Steady State Calculations.” Journal of Computational Physics 144, no. 2 (August 10, 1998): 237–56. https://doi.org/10.1006/jcph.1998.5970.
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    • Xu, E., and J. G. Liu. “Pricing of mortgage-backed securities with option-adjusted spread.” Managerial Finance 24 (1998): 94–109.
    • E, W., and J. G. Liu. “Finite Difference Methods for 3D Viscous Incompressible Flows in the Vorticity-Vector Potential Formulation on Nonstaggered Grids.” Journal of Computational Physics 138, no. 1 (November 15, 1997): 57–82. https://doi.org/10.1006/jcph.1997.5815.
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    • Chen, G. Q., and J. G. Liu. “Convergence of difference schemes with high resolution for conservation laws.” Mathematics of Computation 66, no. 219 (January 1, 1997): 1027–53. https://doi.org/10.1090/s0025-5718-97-00859-4.
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    • Weinan, E., and J. G. Liu. “Finite difference schemes for incompressible flows in the velocity - impulse density formulation.” Journal of Computational Physics 130, no. 1 (January 1, 1997): 67–76. https://doi.org/10.1006/jcph.1996.5537.
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    • Weinan, E., and J. G. Liu. “Vorticity boundary condition and related issues for finite difference schemes.” Journal of Computational Physics 124, no. 2 (March 15, 1996): 368–82. https://doi.org/10.1006/jcph.1996.0066.
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    • Jin, S., and J. G. Liu. “The effects of numerical viscosities: I. Slowly moving shocks.” Journal of Computational Physics 126, no. 2 (January 1, 1996): 373–89. https://doi.org/10.1006/jcph.1996.0144.
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    • Jin, S., and J. G. Liu. “Oscillations induced by numerical viscosities.” Mat. Contemp. 10 (1996): 169–80.
    • Levermore, C. D., and J. G. Liu. “Large oscillations arising in a dispersive numerical scheme.” Physica D: Nonlinear Phenomena 99, no. 2–3 (January 1, 1996): 191–216. https://doi.org/10.1016/S0167-2789(96)00157-1.
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    • Liu, J. G., and Z. Xin. “Boundary layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation.” Arch. Rat. Mech. Anal. 135 (1996): 61–105.
    • Liu, J. G., and Z. Xin. “Kinetic and viscous boundary layers for broadwell equations.” Transport Theory and Statistical Physics 25, no. 3–5 (January 1, 1996): 447–61. https://doi.org/10.1080/00411459608220713.
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    • Weinan, E., and J. G. Liu. “Projection method II: Godunov-Ryabenki analysis.” Siam Journal on Numerical Analysis 33, no. 4 (January 1, 1996): 1597–1621. https://doi.org/10.1137/s003614299426450x.
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    • Weinan, E., and J. G. Liu. “Essentially compact schemes for unsteady viscous incompressible flows.” Journal of Computational Physics 126, no. 1 (January 1, 1996): 122–38. https://doi.org/10.1006/jcph.1996.0125.
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    • Liu, J. ‐., and Z. Xin. “Convergence of vortex methods for weak solutions to the 2‐D euler equations with vortex sheet data.” Communications on Pure and Applied Mathematics 48, no. 6 (January 1, 1995): 611–28. https://doi.org/10.1002/cpa.3160480603.
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    • Weinan, E., and J. G. Liu. “Projection method I: convergence and numerical boundary layers.” Siam J. Numer. Anal. 32 (1995): 1017–57.
    • LEFLOCH, P. G., and J. G. LIU. “DISCRETE ENTROPY AND MONOTONICITY CRITERIA FOR HYPERBOLIC CONSERVATION-LAWS.” Comptes Rendus De L Academie Des Sciences Serie I Mathematique 319, no. 8 (October 20, 1994): 881–86.
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    • Jin, S., and J. G. Liu. “Relaxation and diffusion enhanced dispersive waves.” Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences 446, no. 1928 (January 1, 1994): 555–63. https://doi.org/10.1098/rspa.1994.0120.
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    • CHEN, G. Q., and J. G. LIU. “CONVERGENCE OF 2ND-ORDER SCHEMES FOR ISENTROPIC GAS-DYNAMICS.” Mathematics of Computation 61, no. 204 (October 1, 1993): 607–27. https://doi.org/10.2307/2153243.
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    • Liu, J. G., and Z. Xin. “Nonlinear stability of discrete shocks for systems of conservation laws.” Archive for Rational Mechanics and Analysis 125, no. 3 (September 1, 1993): 217–56. https://doi.org/10.1007/BF00383220.
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    • Engquist, B., and J. ‐. Liu. “Numerical methods for oscillatory solutions to hyperbolic problems.” Communications on Pure and Applied Mathematics 46, no. 10 (January 1, 1993): 1327–61. https://doi.org/10.1002/cpa.3160461003.
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    • Liu, J. G., and Z. Xin. “L¹-stability of stationary discrete shocks.” Mathematics of Computation 60, no. 201 (January 1, 1993): 233–44. https://doi.org/10.1090/S0025-5718-1993-1159170-7.
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    • Liu, Jian-Guo, and Zhouping Xin. “L 1 -Stability of Stationary Discrete Shocks.” Mathematics of Computation 60, no. 201 (January 1993): 233–233. https://doi.org/10.2307/2153163.
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    • Chen, G. Q., and J. G. Liu. “Convergence of second-order schemes for isentropic gas dynamics.” Math. Comp. 61 (1993): 607–29.

  • Conference Papers

    • Frouvelle, A., and J. G. Liu. “Long-Time Dynamics for a Simple Aggregation Equation on the Sphere.” In Springer Proceedings in Mathematics and Statistics, 282:457–79, 2019. https://doi.org/10.1007/978-3-030-15096-9_16.
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    • Liu, J. G., and Y. Zhang. “Convergence of diffusion-drift many particle systems in probability under a sobolev norm.” In Springer Proceedings in Mathematics and Statistics, 162:195–223, 2016. https://doi.org/10.1007/978-3-319-32144-8_10.
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    • Degond, Pierre, Amic Frouvelle, and Jian-Guo Liu. “A NOTE ON PHASE TRANSITIONS FOR THE SMOLUCHOWSKI EQUATION WITH DIPOLAR POTENTIAL.” In Hyperbolic Problems: Theory, Numerics, Applications, edited by F. Ancona, A. Bressan, P. Marcati, and A. Marson, 8:179–92. AMER INST MATHEMATICAL SCIENCES-AIMS, 2014.
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• Teaching & Mentoring
• 

  Recent Courses

  • K_MATH 105: Calculus 2021
  • K_MATH 450: Measure and Integration 2021
  • PHYSICS 762: Electrodynamics 2021
  • MATH 635: Functional Analysis 2020
  • PHYSICS 762: Electrodynamics 2020
  • K_MATH 201: Multivariable Calculus 2019
  • K_PHYS 122: General Physics II 2019
• Scholarly, Clinical, & Service Activities
• 

  Presentations & Appearances

  • Coagulation-Fragmentation model without detailed balance for animal group-size statistics. September 11, 2013  2013
  • Coagulation-Fragmentation model without detailed balance for animal group-size statistics. August 8, 2013  2013
  • Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics. August 1, 2013  2013
  • The dynamic and steady states for multi-dimensional Keller-Segel model with the diffusion exponent m > 0. July 26, 2013  2013
  • Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics. July 15, 2013  2013
  • Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics. June 25, 2013  2013
  • Global weak solution for kinetic models of active swimming and passive suspensions. May 1, 2013  2013
  • The dynamic and steady states for multi-dimensional Keller-Segel model with the diffusion exponent m>0. February 21, 2013  2013
  • Phase transitions for self-organized dynamics and sweeping networks. January 1, 2013  2013
  • Estimate on Laplace-Leray commutator and application to the Navier-Stokes equation in a bounded domain. December 11, 2012  2012
  • Phase transition for Smoluchowski equation. Seminar. Seminar, University of Rennes, France. November 22, 2012  2012
  • Global weak solution for kinetic models of active swimming and passive suspensions. October 9, 2012  2012
  • Phase transition of self-alignment in flocking dynamics. September 7, 2012  2012
  • Multi-dimensional Keller-Segel model with supercritical diffusion exponent. August 7, 2012  2012
  • Multi-dimensional Keller-Segel model with supercritical diffusion exponent. July 17, 2012  2012
  • Viscek flocking dynamics and phase transition. June 28, 2012  2012
  • Bacterium swimming, flocking dynamics and phase transition. June 27, 2012  2012
  • Mathematical analysis of flocking dynamics in biology and social science. June 19, 2012  2012
  • Convergence of a Particle Method and Global Weak Solutions for a Family of Evolutionary PDEs. December 15, 2011  2011
  • Asymptotic-Preserving schemes for kinetic–fluid modeling of disperse two-phase flows. December 8, 2011  2011
  • Global weak solution for kinetic models of active swimming and passive suspensions. November 23, 2011  2011
  • Dynamics of orientational alignment and phase transition. October 20, 2011  2011
  • Pressure boundary condition and projection method. September 1, 2011  2011
  • Hydrodynamics of Vicsek self-alignment interactions. August 2, 2011  2011
  • Multi-dimensional degenerate Keller-Segel system with critical diffusion exponent 2n/(n+2). August 1, 2011  2011
  • Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation. July 13, 2011  2011
  • Dynamics of orientational alignment and phase transition. June 1, 2011  2011
  • Dynamics of orientational alignment and phase transition. April 20, 2011  2011
  • Dynamics of orientational alignment and phase transition. April 6, 2011  2011
  • Dynamics of orientational alignment and phase transition. February 11, 2011  2011
  • Dynamics of orientational alignment and phase transition. February 1, 2011  2011
  • Asymptotic-preserving schemes for some kinetic equations. January 1, 2011  2011
  • Dynamics of orientational alignment and phase transition. December 1, 2010  2010
  • Modeling and analysis of collective behavior of self-propelled agents. December 1, 2010  2010
  • Dynamics of orientational alignment and phase transition. November 18, 2010  2010
  • Dynamics of orientational alignment and phase transition. November 12, 2010  2010
  • Estimate on commutator of the Laplacian and Leray projection operators and application to Navier-Stokes equation in bounded domain. November 12, 2010  2010
  • Modeling and analysis of collective behavior of self-propelled agents. November 11, 2010  2010
  • Dynamics of orientational alignment and phase transition. November 1, 2010  2010
  • Modeling and analysis of collective behavior of self-propelled agents. October 19, 2010  2010
  • Dynamics of orientational alignment and phase transition. October 1, 2010  2010
  • Analysis of dynamics of Doi-Onsager phase transition. September 29, 2010  2010
  • Analysis of Dynamics of Doi-Onsager Phase Transition. September 6, 2010  2010
  • Estimate on commutator of the Laplacian and Leray projection operators and application to Navier-Stokes equation in bounded domain. September 3, 2010  2010
  • Asymptotic-preserving schemes for some kinetic equations. August 31, 2010  2010
  • Some estimates on collective behavior of self-propelled biological agents. December 3, 2009  2009
  • Asymptotic-preserving schemes for fluids equations and kinetic equations. November 17, 2009  2009
  • Modeling and analysis of collective behavior of self-propelled agents. November 6, 2009  2009
  • The challenge of simulating fluid flow accurately in the presence of boundaries. November 5, 2009  2009
  • Analysis and computation of Navier–Stokes equation in bounded domains. October 5, 2009  2009
  • Modeling and analysis of collective behavior of self-propelled agents. September 4, 2009  2009
  • Controlling numerical dissipation and time stepping in some multi-scale kinetic/fluid simulations. September 1, 2009  2009
  • Modeling and analysis of collective behavior of self-propelled agents. August 19, 2009  2009
  • Some numerical analysis issues in material and fluids simulations. August 1, 2009  2009
  • A simple proof of the Cucker-Smale flocking dynamics and mean-field limit. July 1, 2009  2009
  • A simple proof of the Cucker-Smale flocking dynamics and mean-field limit. July 1, 2009  2009
  • Asymptotic-preserving schemes for fluids equations and kinetic equations. June 9, 2009  2009
  • The challenge of simulating fluid flow accurately in the presence of boundaries. June 8, 2009  2009
  • Pressure and projection methods for viscous incompressible flows. May 11, 2009  2009
  • A new approach in analysis and computation of Navier-Stokes equation in bounded domain. March 12, 2009  2009
  • The challenge of simulating incompressible fluid flow accurately in the presence of boundaries. January 30, 2009  2009
  • All speed asymptotic-preserving schemes for compressible flows. August 1, 2008  2008
  • A simple proof of Cucker-Smale flocking dynamics and the mean field limit. July 25, 2008  2008
  • A simple proof of Cucker-Smale flocking dynamics and the mean field limit}. July 24, 2008  2008
  • Mach number uniform asymptotic preserving schemes for fluids and plasmas. July 14, 2008  2008
  • The challenge of simulating incompressible fluid flow accurately in the presence of boundaries. May 9, 2008  2008
  • The challenge of simulating incompressible fluid flow accurately in the presence of boundaries. May 6, 2008  2008
  • A simple proof of the Cucker-Smale flocking dynamics and mean-field limit,. April 1, 2008  2008
  • Computation of incompressible flow past a sphere and local behavior of boundary layer separation. April 1, 2008  2008
  • A simple proof of Cucker-Smale flocking dynamics and the mean field limit. March 21, 2008  2008
  • On computation of incompressible flow past a sphere. March 10, 2008  2008
  • Finite element Navier-Stokes solvers based on an unconstrained reformulation. March 4, 2008  2008
  • Finite element Navier-Stokes solvers based on an unconstrained reformulation. February 22, 2008  2008
• 

  Outreach & Engaged Scholarship

  • Unknown. Promotion and tenure external evaluators for various universities. January 1, 2012  2012
• 

  Service to the Profession

  • Co-organized SIAM Conference on Analysis of Partial Differential Equations, mini-symposium: Asymptotically Preserving Numerical Methods for Time-Depe. December 22, 2013  2013
  • Co-organized SIAM PDE13 mini-symposium: Asymptotically Preserving Numerical Methods for Time-Dependent PDEs. December 22, 2013  2013
  • Chair of the international committee for the oral exam in the section Applied and Computational Mathematics for S. T. Yau College Mathematics Contests. 2013  2013
  • Member of the Steering Committee for the Tsinghua Sanya International Mathematics Forum. 2013  2013
  • Member of the Steering Committee for the Tsinghua Sanya International Mathematics Forum. 2013  2013
  • Refereed for a number of journals. 2013  2013
  • Refereed for a number of journals. 2013  2013
  • Promotion and tenure external evaluators for various universities. July 1, 2012  2012
  • Tutorial Lectures for Program: "Partial Differential Equations in Kinetic Theories", Newton Institute, Cambridge, UK. August 2010 - September 2010  2010
  • panelist : NSF Numerical Methods (P100833) panel. March 2010  2010
  • Organizer Committee : IMA Workshop on Analysis and Computation of Incompressible Fluid Flow. February 2010  2010
  • exterior doctoral committee for Baver Okutmustur, University Paris VI. 2010  2010
  • Organizer Committee, Singapore : Two Month Program on Mathematical Theory and Numerical Methods for Computational Materials Simulation and Design. July 1, 2009 - August 30, 2009  2009
  • Organizer Committee, Singapore : Two Month Program on Mathematical Theory and Numerical Methods for Computational Materials Simulation and Design. July 2009 - August 2009  2009

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