Scholars@Duke

• Background
• 

  Education, Training, & Certifications

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

  In the News

  • NOV 21, 2016

    Liu Named Fellow of the American Mathematical Society
• Expertise
• 

  Global Scholarship

  • Teaching

    • China (Country) 
• Research
• 

  Selected Grants

  • 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

    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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). https://doi.org/10.1038/s41598-019-48023-5.
       Full Text  Open Access Copy  Link to Item
    • 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.
       Full Text
    • Zhan, Qiwei, Mingwei Zhuang, Zhennan Zhou, Jian-Guo Liu, and Qing Huo 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 2019): 4591–99. https://doi.org/10.1109/tgrs.2019.2891691.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text  Open Access Copy
    • 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.
       Full Text
    • 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). https://doi.org/10.1098/rspa.2018.0610.
       Full Text
    • 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). https://doi.org/10.1088/1361-6560/aaf5a5.
       Full Text  Open Access Copy  Link to Item
    • 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.
       Full Text
    • Gao, Yuan, Jian-Guo Liu, and Xin Yang Lu. “Gradient flow approach to an exponential thin film equation: global existence and latent singularity.” Esaim: Control, Optimisation and Calculus of Variations 25 (2019): 49–49. https://doi.org/10.1051/cocv/2018037.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text  Open Access Copy
    • 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.
       Full Text  Open Access Copy
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • Liu, Jian-Guo, and Xiangsheng 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.
       Full Text  Link to Item
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.a7.
       Full Text
    • 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.
       Full Text
    • Gao, Yu, and Jian-Guo Liu. “The modified Camassa-Holm equation in Lagrangian coordinates.” Discrete & Continuous Dynamical Systems  B 23, no. 6 (2018): 2545–92. https://doi.org/10.3934/dcdsb.2018067.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text  Open Access Copy
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text  Open Access Copy
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text  Open Access Copy
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text  Open Access Copy
    • 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.
       Full Text
    • 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 (January 1, 2015): 63–115. https://doi.org/10.1007/s00205-014-0800-7.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • Jin, S., J. G. Liu, and L. Wang. “A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations.” Mathematics of Computation 82, no. 282 (February 7, 2013): 749–79. https://doi.org/10.1090/S0025-5718-2012-02643-3.
       Full Text
    • 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.
    • Haack, J., S. Jin, and J. G. Liu. “An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equations.” Communications in Computational Physics 12, no. 4 (October 1, 2012): 955–80. https://doi.org/10.4208/cicp.250910.131011a.
       Full Text
    • Chae, D., and J. G. Liu. “Blow-up, Zero α Limit and the Liouville Type Theorem for the Euler-Poincaré Equations.” Communications in Mathematical Physics 314, no. 3 (September 1, 2012): 671–87. https://doi.org/10.1007/s00220-012-1534-8.
       Full Text
    • Carrillo, J. A., L. Chen, J. G. Liu, and J. Wang. “A note on the subcritical two dimensional Keller-Segel system.” Acta Applicandae Mathematicae 119, no. 1 (June 1, 2012): 43–55. https://doi.org/10.1007/s10440-011-9660-4.
       Full Text
    • Chen, L., J. G. Liu, and J. Wang. “Multidimensional degenerate Keller-Segel system with critical diffusion exponent 2n/(n + 2).” Siam Journal on Mathematical Analysis 44, no. 2 (May 28, 2012): 1077–1102. https://doi.org/10.1137/110839102.
       Full Text
    • Chertock, A., J. G. Liu, and T. Pendleton. “Convergence of a particle method and global weak solutions of a family of evolutionary PDEs.” Siam Journal on Numerical Analysis 50, no. 1 (May 28, 2012): 1–21. https://doi.org/10.1137/110831386.
       Full Text
    • Frouvelle, A., and J. G. Liu. “Dynamics in a kinetic model of oriented particles with phase transition.” Siam Journal on Mathematical Analysis 44, no. 2 (May 28, 2012): 791–826. https://doi.org/10.1137/110823912.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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, no. 4 (December 1, 2011): 901–18. https://doi.org/10.3934/krm.2011.4.901.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • Liu, J. G., and A. Lorz. “A coupled chemotaxis-fluid model: Global existence.” Annales De L’Institut Henri Poincare (C) Analyse Non Lineaire 28, no. 5 (January 1, 2011): 643–52. https://doi.org/10.1016/j.anihpc.2011.04.005.
       Full Text
    • Liu, Jian-Guo, and Robert L. Pego. “STABLE DISCRETIZATION OF MAGNETOHYDRODYNAMICS IN BOUNDED DOMAINS.” Communications in Mathematical Sciences 8, no. 1 (March 1, 2010): 234–51.
       Link to Item
    • 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.
       Full Text
    • Liu, J. G., and L. Mieussens. “Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit.” Siam Journal on Numerical Analysis 48, no. 4 (January 1, 2010): 1474–91. https://doi.org/10.1137/090772770.
       Full Text  Open Access Copy
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • Ha, S. Y., and J. G. Liu. “A simple proof of the Cucker-Smale flocking dynamics and mean-field limit.” Communications in Mathematical Sciences 7, no. 2 (January 1, 2009): 297–325. https://doi.org/10.4310/CMS.2009.v7.n2.a2.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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 (June 1, 2004): 267–90.
    • 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.
       Full Text
    • Li, B., and J. G. Liu. “Eptaxial growth without slope selection: energetics, coarsening, and dynamic scaling.” J. Nonlinear Sci. 14 (2004): 429–51.
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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 (May 1, 2003): 201–28.
    • Liu, JG, Wang, C, and Johnston, H. "A Fourth Order Scheme for Incompressible Boussinesq Equations." Journal of Scientific Computing 18, no. 2 (April 1, 2003): 253-285.  Full Text
    • 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.
       Full Text
    • 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. “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.
    • Duraisamy, K, Baeder, JD, and Liu, J-G. "Concepts and Application of Time-Limiters to High Resolution Schemes." Journal of Scientific Computing 19, no. 1-3 (2003): 139-162.  Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • Wang, C., and J. G. Liu. “Convergence of gauge method for incompressible flow.” Mathematics of Computation 69, no. 232 (October 1, 2000): 1385–1407.
    • 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.
       Full Text  Link to Item
    • 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.
       Full Text
    • 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.
       Full Text
    • Lefloch, P. G., and J. G. Liu. “Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions.” Mathematics of Computation 68, no. 227 (July 1, 1999): 1025–55.
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • Chen, G. Q., and J. G. Liu. “Convergence of difference schemes with high resolution for conservation laws.” Mathematics of Computation 66, no. 219 (July 1, 1997): 1027–53.
    • 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.
    • Liu, J. G., and Z. Xin. “Boundary-layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation.” Archive for Rational Mechanics and Analysis 135, no. 1 (October 18, 1996): 61–105. https://doi.org/10.1007/BF02198435.
       Full Text
    • Weinan, E., and J. G. Liu. “Projection method II: Godunov-Ryabenki analysis.” Siam Journal on Numerical Analysis 33, no. 4 (August 1, 1996): 1597–1621.
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • E, Weinan, and Jian-Guo Liu. “Projection Method I: Convergence and Numerical Boundary Layers.” Siam Journal on Numerical Analysis 32, no. 4 (August 1995): 1017–57. https://doi.org/10.1137/0732047.
       Full Text
    • 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.
       Full Text
    • 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.
       Link to Item
    • 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 (September 8, 1994): 555–63.
    • 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.
       Full Text  Link to Item
    • 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.
       Full Text
    • Chen, G. Q., and J. G. Liu. “Convergence of second-order schemes for isentropic gas dynamics.” Mathematics of Computation 61, no. 204 (January 1, 1993): 607–27. https://doi.org/10.1090/S0025-5718-1993-1185239-7.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Full Text
    • Huang, Hui, Jian-Guo Liu, and Peter Pickl. “On the mean-field limit for the Vlasov-Poisson-Fokker-Planck system,” n.d.
       Open Access Copy  Link to Item

  • 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.
       Full Text
    • 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.
       Full Text
    • 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.
       Link to Item
• Teaching & Mentoring
• 

  Recent Courses

  • PHYSICS 762: Electrodynamics 2020
  • K_INTGSC 101: Integrated Science 1 2018
  • K_MATH 101: Mathematical Foundations 1 2018
• 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

Some information on this profile has been compiled automatically from Duke databases and external sources. (Our About page explains how this works.) If you see a problem with the information, please write to Scholars@Duke and let us know. We will reply promptly.