Jian-Guo Liu | Scholars@Duke

Jian-Guo Liu
Professor of Physics

Current Appointments & Affiliations

Professor of Physics, Physics, Trinity College of Arts & Sciences 2009
Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2009

Contact Information

285 Physics Bldg, Durham, NC 27708
Box 90320, Durham, NC 27708-0320
jian-guo.liu@duke.edu (919) 660-2500
http://www.math.duke.edu/~jliu/

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
- Conference Papers
  - Liu, JG, and Zhang, Y. "Convergence of diffusion-drift many particle systems in probability under a sobolev norm." January 1, 2016. Full Text
  - Degond, P, Frouvelle, A, and Liu, J-G. "A NOTE ON PHASE TRANSITIONS FOR THE SMOLUCHOWSKI EQUATION WITH DIPOLAR POTENTIAL." 2014. Link to Item
- Journal Articles
  - Feng, Y, Li, L, Liu, J-G, and Xu, X. "A note on one-dimensional time fractional ODEs." Applied Mathematics Letters 83 (September 2018): 87-94. Full Text
  - Li, L, Liu, J-G, and Wang, L. "Cauchy problems for Keller–Segel type time–space fractional diffusion equation." Journal of Differential Equations 265, no. 3 (August 2018): 1044-1096. Full Text
  - Chen, K, Li, Q, and Liu, J-G. "Online learning in optical tomography: a stochastic approach." Inverse Problems 34, no. 7 (July 1, 2018): 075010-075010. Full Text
  - Liu, JG, Tang, M, Wang, L, and Zhou, Z. "An accurate front capturing scheme for tumor growth models with a free boundary limit." Journal of Computational Physics 364 (July 1, 2018): 73-94. Full Text
  - Liu, J-G, and Xu, X. "Partial regularity of weak solutions to a PDE system with cubic nonlinearity (Accepted)." JOURNAL OF DIFFERENTIAL EQUATIONS 264, no. 8 (April 15, 2018): 5489-5526. Full Text Link to Item
  - Gao, Y, Liu, J-G, Lu, XY, and Xu, X. "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 2018). Full Text
  - Li, L, and Liu, J-G. "p -Euler equations and p -Navier–Stokes equations." Journal of Differential Equations 264, no. 7 (April 2018): 4707-4748. Full Text
  - Liu, J-G, and Xu, X. "Partial regularity of weak solutions to a PDE system with cubic nonlinearity." Journal of Differential Equations 264, no. 8 (April 2018): 5489-5526. Full Text
  - Feng, Y, Li, L, and Liu, JG. "Semigroups of stochastic gradient descent and online principal component analysis: Properties and diffusion approximations." Communications in Mathematical Sciences 16, no. 3 (January 1, 2018): 777-789. Full Text
  - Gao, Y, Li, L, and Liu, J-G. "A Dispersive Regularization for the Modified Camassa--Holm Equation." Siam Journal on Mathematical Analysis 50, no. 3 (January 2018): 2807-2838. Full Text
  - Li, L, and Liu, J-G. "A Generalized Definition of Caputo Derivatives and Its Application to Fractional ODEs." Siam Journal on Mathematical Analysis 50, no. 3 (January 2018): 2867-2900. Full Text
  - Li, L, and Liu, J-G. "SOME COMPACTNESS CRITERIA FOR WEAK SOLUTIONS OF TIME FRACTIONAL PDEs." Siam Journal on Mathematical Analysis 50, no. 4 (January 1, 2018): 3963-3995. (Academic Article) Full Text Link to Item
  - Li, L, Liu, J-G, and Lu, J. "Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem." Journal of Statistical Physics 169, no. 2 (October 2017): 316-339. Full Text Open Access Copy
  - Liu, J-G, Wang, L, and Zhou, Z. "Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations." Mathematics of Computation 87, no. 311 (September 19, 2017): 1165-1189. Full Text
  - Coquel, F, Jin, S, Liu, J-G, and Wang, L. "Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and Glimm front sampling for scalar conservation laws." Mathematics of Computation 87, no. 311 (September 7, 2017): 1083-1126. Full Text
  - Gao, Y, Ji, H, Liu, J-G, and Witelski, TP. "Global existence of solutions to a tear film model with locally elevated evaporation rates." Physica D: Nonlinear Phenomena 350 (July 2017): 13-25. Full Text
  - Liu, J-G, Ma, Z, and Zhou, Z. "Explicit and Implicit TVD Schemes for Conservation Laws with Caputo Derivatives." Journal of Scientific Computing 72, no. 1 (July 2017): 291-313. Full Text
  - Gao, Y, Liu, J-G, and Lu, J. "Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces." Journal of Nonlinear Science 27, no. 3 (June 2017): 873-926. Full Text Open Access Copy
  - Degond, P, Liu, J-G, and Pego, RL. "Coagulation–Fragmentation Model for Animal Group-Size Statistics." Journal of Nonlinear Science 27, no. 2 (April 2017): 379-424. Full Text
  - Huang, H, and Liu, J-G. "Error estimate of a random particle blob method for the Keller-Segel equation." Mathematics of Computation 86, no. 308 (February 15, 2017): 2719-2744. Full Text
  - Liu, J-G, and Wang, J. "Global existence for a thin film equation with subcritical mass." Discrete and Continuous Dynamical Systems - Series B 22, no. 4 (February 2017): 1461-1492. Full Text
  - Degond, P, Herty, M, and Liu, J-G. "Mean-field games and model predictive control." Communications in Mathematical Sciences 15, no. 5 (2017): 1403-1422. Full Text
  - Degond, P, Liu, J-G, Merino-Aceituno, S, and Tardiveau, T. "Continuum dynamics of the intention field under weakly cohesive social interaction." Mathematical Models and Methods in Applied Sciences 27, no. 01 (January 2017): 159-182. Full Text
  - Gao, Y, Ji, H, Liu, J-G, and P. Witelski, T. "A vicinal surface model for epitaxial growth with logarithmic free energy." Discrete & Continuous Dynamical Systems B 22, no. 11 (2017): 1-21. Full Text
  - Gao, Y, Liu, J-G, and Lu, J. "Weak Solution of a Continuum Model For Vicinal Surface in The Attachment-Detachment-Limited Regime." SIAM Journal on Mathematical Analysis 49, no. 3 (January 2017): 1705-1731. Full Text Open Access Copy
  - Gao, Y, and Liu, J-G. "Global Convergence of a Sticky Particle Method for the Modified Camassa--Holm Equation." SIAM Journal on Mathematical Analysis 49, no. 2 (January 2017): 1267-1294. Full Text
  - Huang, H, and Liu, J-G. "Discrete-in-time random particle blob method for the Keller–Segel equation and convergence analysis." Communications in Mathematical Sciences 15, no. 7 (2017): 1821-1842. Full Text
  - Li, L, and Liu, J-G. "A note on deconvolution with completely monotone sequences and discrete fractional calculus." Quarterly of Applied Mathematics (2017): 1-1. Full Text
  - Liu, J-G, and Wang, J. "A generalized Sz. Nagy inequality in higher dimensions and the critical thin film equation." Nonlinearity 30, no. 1 (January 1, 2017): 35-60. Full Text
  - Liu, J-G, and Xu, X. "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 2017): 2220-2245. Full Text
  - Liu, J-G, and Cong, W. "Uniform $L^{\infty}$ boundedness for a degenerate parabolic-parabolic Keller-Segel model." Discrete and Continuous Dynamical Systems - Series B 22, no. 2 (December 2016): 307-338. Full Text
  - Huang, H, and Liu, J-G. "A note on Monge–Ampère Keller–Segel equation." Applied Mathematics Letters 61 (November 2016): 26-34. Full Text
  - Huang, H, and Liu, J-G. "Error estimates of the aggregation-diffusion splitting algorithms for the Keller-Segel equations." Discrete and Continuous Dynamical Systems - Series B 21, no. 10 (November 2016): 3463-3478. Full Text
  - Liu, J-G, and Cong, W. "A degenerate $p$-Laplacian Keller-Segel model." Kinetic and Related Models 9, no. 4 (September 2016): 687-714. Full Text
  - Liu, J-G, and Huang, H. "Well-posedness for the Keller-Segel equation with fractional Laplacian and the theory of propagation of chaos." Kinetic and Related Models 9, no. 4 (September 2016): 715-748. Full Text
  - Liu, J-G, and Yang, R. "A random particle blob method for the Keller-Segel equation and convergence analysis." Mathematics of Computation 86, no. 304 (May 17, 2016): 725-745. Full Text
  - Herschlag, G, Liu, J-G, and Layton, AT. "Fluid extraction across pumping and permeable walls in the viscous limit." Physics of Fluids 28, no. 4 (April 2016): 041902-041902. Full Text
  - Liu, J-G, and Wang, J. "A Note on L ∞ $L^{\infty}$ -Bound and Uniqueness to a Degenerate Keller-Segel Model." Acta Applicandae Mathematicae 142, no. 1 (April 2016): 173-188. Full Text
  - Liu, J-G, and Pego, RL. "On generating functions of Hausdorff moment sequences." Transactions of the American Mathematical Society 368, no. 12 (February 2, 2016): 8499-8518. Full Text
  - Liu, J-G, and Wang, J. "Refined hyper-contractivity and uniqueness for the Keller–Segel equations." Applied Mathematics Letters 52 (February 2016): 212-219. Full Text
  - Chen, J, Liu, J-G, and Zhou, Z. "On a Schrödinger--Landau--Lifshitz System: Variational Structure and Numerical Methods." Multiscale Modeling & Simulation 14, no. 4 (January 2016): 1463-1487. Full Text
  - Liu, J-G, and Xu, X. "Existence Theorems for a Multidimensional Crystal Surface Model." SIAM Journal on Mathematical Analysis 48, no. 6 (January 2016): 3667-3687. Full Text
  - Xue, Y, Wang, C, and Liu, J-G. "Simple Finite Element Numerical Simulation of Incompressible Flow Over Non-rectangular Domains and the Super-Convergence Analysis." Journal of Scientific Computing 65, no. 3 (December 2015): 1189-1216. Full Text
  - Chertock, A, Liu, J-G, and Pendleton, T. "Elastic collisions among peakon solutions for the Camassa–Holm equation." Applied Numerical Mathematics 93 (July 2015): 30-46. Full Text
  - Degond, P, Frouvelle, A, and Liu, J-G. "Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics." Archive for Rational Mechanics and Analysis 216, no. 1 (April 2015): 63-115. Full Text
  - Lu, J, Liu, J-G, and Margetis, D. "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): 032403-. Full Text Open Access Copy
  - Chertock, A, Liu, JG, and Pendleton, T. "Elastic collisions among peakon solutions for the Camassa-Holm equation." Applied Numerical Mathematics 93 (January 1, 2015): 30-46. Full Text
  - Degond, P, Frouvelle, A, and Liu, JG. "Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics." Archive for Rational Mechanics and Analysis 216, no. 1 (January 1, 2015): 63-115. Full Text
  - Herschlag, G, Liu, J-G, and Layton, AT. "An Exact Solution for Stokes Flow in a Channel with Arbitrarily Large Wall Permeability." SIAM Journal on Applied Mathematics 75, no. 5 (January 2015): 2246-2267. Full Text
  - Coquel, F, Jin, S, Liu, J-G, and Wang, L. "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 (December 2014): 1051-1084. Full Text
  - Degond, P, Liu, J-G, and Ringhofer, C. "Evolution of wealth in a non-conservative economy driven by local Nash equilibria." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2028 (October 6, 2014): 20130394-20130394. Full Text
  - Johnston, H, Wang, C, and Liu, J-G. "A Local Pressure Boundary Condition Spectral Collocation Scheme for the Three-Dimensional Navier–Stokes Equations." Journal of Scientific Computing 60, no. 3 (September 2014): 612-626. Full Text
  - Goudon, T, Jin, S, Liu, J-G, and Yan, B. "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. Full Text
  - Goudon, T, Jin, S, Liu, JG, and Yan, B. "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. Full Text
  - Chae, D, Degond, P, and Liu, J-G. "Well-posedness for Hall-magnetohydrodynamics." Annales De L'Institut Henri Poincare (C) Non Linear Analysis 31, no. 3 (May 2014): 555-565. Full Text
  - Duan, Y, and Liu, JG. "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. Full Text
  - Degond, P, Liu, JG, and Ringhofer, C. "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): 751-780. Full Text
  - Chae, D, Degond, P, and Liu, JG. "Well-posedness for hall-magnetohydrodynamics." Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire 31, no. 3 (January 1, 2014): 555-565. Full Text
  - Chen, X, Jüngel, A, and Liu, JG. "A note on Aubin-Lions-Dubinskiǐ Lemmas." Acta Applicandae Mathematicae 133, no. 1 (January 1, 2014): 33-43. Full Text
  - Chen, X, Li, X, and Liu, J-G. "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 (2014): 1579-1601. Full Text
  - Coquel, F, Jin, S, Liu, JG, and Wang, L. "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): 1051-1084. Full Text
  - Degond, P, Herty, M, and Liu, J-G. "Flow on Sweeping Networks." Multiscale Modeling & Simulation 12, no. 2 (January 2014): 538-565. Full Text
  - Degond, P, Liu, JG, and Ringhofer, C. "Large-scale dynamics of mean-field games driven by local nash equilibria." Journal of Nonlinear Science 24, no. 1 (January 1, 2014): 93-115. Full Text
  - Johnston, H, Wang, C, and Liu, J-G. "A Local Pressure Boundary Condition Spectral Collocation Scheme for the Three-Dimensional Navier–Stokes Equations." Journal of Scientific Computing 60, no. 3 (2014): 612-626. Full Text
  - Zou, C, Liu, J-G, and Bian, S. "Ultra-contractivity for Keller-Segel model with diffusion exponent $m>1-2/d$." Kinetic and Related Models 7, no. 1 (December 2013): 9-28. Full Text
  - Huang, YL, Liu, JG, and Wang, WC. "A generalized mac scheme on curvilinear domains." SIAM Journal on Scientific Computing 35, no. 5 (November 7, 2013). Full Text
  - Bian, S, and Liu, JG. "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): 1017-1070. Full Text
  - Bian, S, and Liu, J-G. "Dynamic and Steady States for Multi-Dimensional Keller-Segel Model with Diffusion Exponent m > 0." Communications in Mathematical Physics (2013): 1-54. Full Text
  - Chen, X, Jüngel, A, and Liu, J-G. "A Note on Aubin-Lions-Dubinskiǐ Lemmas." Acta Applicandae Mathematicae (2013): 1-11.
  - Chen, X, and Liu, J-G. "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 (2013): 2764-2802. Full Text
  - Chen, X, and Liu, J-G. "Analysis of polymeric flow models and related compactness theorems in weighted spaces." SIAM Journal on Mathematical Analysis 45, no. 3 (2013): 1179-1215. Full Text
  - Degond, P, Frouvelle, A, and Liu, J-G. "Macroscopic limits and phase transition in a system of self-propelled particles." Journal of Nonlinear Science 23, no. 3 (2013): 427-456. Full Text
  - Degond, P, Liu, J-G, and Ringhofer, C. "Evolution of the Distribution of Wealth in an Economic Environment Driven by Local Nash Equilibria." Journal of Statistical Physics (2013): 1-30.
  - Degond, P, Liu, J-G, and Ringhofer, C. "Large-Scale Dynamics of Mean-Field Games Driven by Local Nash Equilibria." Journal of Nonlinear Science (2013): 1-23. Full Text
  - Goudon, T, Jin, S, Liu, J-G, and Yan, B. "Asymptotic-preserving schemes for kinetic-fluid modeling of disperse two-phase flows." Journal of Computational Physics 246 (2013): 145-164. Full Text
  - Haack, J, Jin, S, and Liu, J. "An All-Speed Asymptotic-Preserving Method for the Isentropic Euler and Navier-Stokes Equations." Communications in Computational Physics 12, no. 04 (October 2012): 955-980. Full Text
  - Carrillo, JA, Chen, L, Liu, J-G, and Wang, J. "A note on the subcritical two dimensional Keller-Segel system." Acta Applicandae Mathematicae 119, no. 1 (2012): 43-55. Full Text
  - Chae, D, and Liu, J-G. "Blow-up, Zero α Limit and the Liouville Type Theorem for the Euler-Poincaré Equations." Communications in Mathematical Physics 314, no. 3 (2012): 671-687. Full Text
  - Chen, L, Liu, J-G, and Wang, J. "Multidimensional Degenerate Keller–Segel System with Critical Diffusion Exponent $2n/(n+2)$." Siam Journal on Mathematical Analysis 44, no. 2 (January 2012): 1077-1102. Full Text
  - Chen, X, and Liu, J-G. "Two nonlinear compactness theorems in L ^p(0,T;B)." Applied Mathematics Letters 25, no. 12 (2012): 2252-2257. Full Text
  - Chertock, A, Liu, J-G, and Pendleton, T. "Convergence of a particle method and global weak solutions of a family of evolutionary PDEs." SIAM Journal on Numerical Analysis 50, no. 1 (2012): 1-21. Full Text
  - Degond, P, Frouvelle, A, and Liu, J-G. "Macroscopic Limits and Phase Transition in a System of Self-propelled Particles." Journal of Nonlinear Science (2012): 1-30. Full Text
  - Degond, P, and Liu, J-G. "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 (2012). Full Text
  - Frouvelle, A, and Liu, J-G. "Dynamics in a kinetic model of oriented particles with phase transition." SIAM Journal on Mathematical Analysis 44, no. 2 (2012): 791-826. Full Text
  - Acheritogaray, M, Degond, P, Frouvelle, A, and Liu, J-G. "Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system." Kinetic and Related Models 4, no. 4 (November 2011): 901-918. Full Text
  - Liu, J-G, and Lorz, A. "A coupled chemotaxis-fluid model: Global existence." Annales De L'Institut Henri Poincare (C) Non Linear Analysis 28, no. 5 (September 2011): 643-652. Full Text
  - Huang, Y-L, Liu, J-G, and Wang, W-C. "An FFT based fast poisson solver on spherical shells." Communications in Computational Physics 9, no. 3 (2011): 649-667. Full Text
  - Jin, S, Liu, J-G, and Wang, L. "A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations (Accepted)." Math. Comp. (2011). (Academic Article)
  - Zheng, W, Gao, H, Liu, J-G, Zhang, Y, Ye, Q, and Swank, C. "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 (2011). Full Text
  - Liu, J-G, Liu, J, and Pego, RL. "Stable and accurate pressure approximation for unsteady incompressible viscous flow." Journal of Computational Physics 229, no. 9 (May 2010): 3428-3453. Full Text
  - Liu, J-G, and Mieussens, L. "Analysis of an Asymptotic Preserving Scheme for Linear Kinetic Equations in the Diffusion Limit." Siam Journal on Numerical Analysis 48, no. 4 (January 2010): 1474-1491. Full Text Open Access Copy
  - Liu, J-G, and Pego, R. "Stable discretization of magnetohydrodynamics in bounded domains." Commun. Math. Sci. 8 (2010): 234-251. (Academic Article)
  - Liu, J-G, and Pego, RL. "Stable discretization of magnetohydrodynamics in bounded domains." Communications in Mathematical Sciences 8, no. 1 (2010): 235-251.
  - Ha, S-Y, and Liu, J-G. "A simple proof of the Cucker-Smale flocking dynamics and mean-field limit." Communications in Mathematical Sciences 7, no. 2 (2009): 297-325. Full Text
  - Liu, J-G, Liu, J, and Pego, RL. "Error estimates for finite-element Navier-Stokes solvers without standard Inf-Sup conditions." Chinese Annals of Mathematics. Series B 30, no. 6 (2009): 743-768. Full Text
  - Liu, J-G, and Wang, W-C. "Characterization and regularity for axisymmetric solenoidal vector fields with application to navier-stokes equation." SIAM Journal on Mathematical Analysis 41, no. 5 (2009): 1825-1850. Full Text
  - Degond, P, Liu, J-G, and Vignal, M-H. "Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit." SIAM Journal on Numerical Analysis 46, no. 3 (2008): 1298-1322. Full Text
  - Hsia, C-H, Liu, J-G, and Wang, C. "Structural stability and bifurcation for 2D incompressible ows with symmetry." Meth. Appl. Anal. 15 (2008): 495-512. (Academic Article)
  - Lin, P, Liu, J-G, and Lu, X. "Long time numerical solution of the Navier-Stokes equations based on a sequential regularization formulation." SIAM Journal on Scientific Computing 31, no. 1 (2008): 398-419. Full Text
  - Liu, J-G, and Wang, C. "A fourth order numerical method for the primtive equations formulated in mean vorticity." Communications in Computational Physics 4, no. 1 (2008): 26-55.
  - Lu, X, Lin, P, and Liu, J-G. "Analysis of a sequential regularization method for the unsteady Navier-Stokes equations." Mathematics of Computation 77, no. 263 (2008): 1467-1494. Full Text
  - Liu, J-G, Liu, J, and Pego, RL. "Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate." Communications on Pure and Applied Mathematics 60, no. 10 (October 2007): 1443-1487. Full Text
  - Antman, SS, and Liu, J-G. "Basic themes and pretty problems of nonlinear solid mechanics." Milan Journal of Mathematics 75, no. 1 (2007): 135-176. Full Text
  - Degond, P, Jin, S, and Liu, JG. "Mach-number uniform asymptotic- preserving Gauge schemes for compressible flows." Bulletin of the Institute of Mathematics Academia Sinica (New Series) 2 (2007): 851-892. (Academic Article)
  - Liu, J-G, Liu, J, and Pego, R. "Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate via a commutator estimate." Comm. Pure Appl. Math. 60 (2007): 1443-1487. (Academic Article)
  - Moore, J, Cheng, Z, Hao, J, Guo, G, Liu, J-G, Lin, C, and Yu, L. "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 (2007): 10173-10182. Full Text
  - Moore, J, Liu, J-G, Zhou, K, and Yu, LL. "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): 5313-5322. Full Text
  - Degond, P, Liu, J-G, and Mieussens, L. "Macroscopic fluid models with localized kinetic upscaling effects." Multiscale Modeling and Simulation 5, no. 3 (2006): 940-979. Full Text
  - Liu, J-G, Samelson, R, and Wang, C. "Global weak solution of planetary geostrophic equations with inviscid geostrophic balance." Applicable Analysis 85 (2006): 593-605. (Academic Article)
  - Liu, J-G, and Wang, W-C. "Convergence analysis of the energy and helicity preserving scheme for axisymmetric flows." SIAM Journal on Numerical Analysis 44, no. 6 (2006): 2456-2480. Full Text
  - Li, B, and Liu, J-G. "Epitaxial Growth Without Slope Selection: Energetics, Coarsening, and Dynamic Scaling." Journal of Nonlinear Science 14, no. 5 (October 2004): 429-451. Full Text
  - Johnston, H, and Liu, J-G. "Accurate, stable and efficient Navier–Stokes solvers based on explicit treatment of the pressure term." Journal of Computational Physics 199, no. 1 (September 2004): 221-259. Full Text
  - Ghil, M, Liu, J-G, Wang, C, and Wang, S. "Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow." Physica D: Nonlinear Phenomena 197, no. 1-2 (2004): 149-173. Full Text
  - Li, B, and Liu, J-G. "Eptaxial growth without slope selection: energetics, coarsening, and dynamic scaling." J. Nonlinear Sci. 14 (2004): 429-451. (Academic Article)
  - Lin, H-E, Liu, J-G, and Xu, W-Q. "Effects of small viscosity and far field boundary conditions for hyperbolic systems." Communications on Pure and Applied Analysis 3, no. 2 (2004): 267-290.
  - Liu, J-G, and Wang, C. "High order finite difference method for unsteady incompressible flow on multi-connected domain in vorticity-stream function formulation." Computer and Fluids 33 (2004): 223-255. (Academic Article)
  - Liu, J-G, and Wang, C. "High order finite difference methods for unsteady incompressible flows in multi-connected domains." Computers and Fluids 33, no. 2 (2004): 223-255. Full Text
  - Liu, J-G, and Wang, W-C. "Energy and helicity preserving schemes for hydro- and magnetohydro-dynamics flows with symmetry." Journal of Computational Physics 200, no. 1 (2004): 8-33. Full Text
  - Liu, J-G, and Xu, W-Q. "Far field boundary condition for convection diffusion equation at zero viscosity limit." Quarterly of Applied Mathematics 62, no. 1 (2004): 27-52.
  - Wang, C, Liu, J-G, and Johnston, H. "Analysis of a fourth order finite difference method for the incompressible Boussinesq equations." Numerische Mathematik 97, no. 3 (2004): 555-594. Full Text
  - LI, B, and LIU, J-G. "Thin film epitaxy with or without slope selection." European Journal of Applied Mathematics 14, no. 6 (December 2003): 713-743. Full Text
  - 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, Liu, J-G, and Peng, Y-J. "Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis." Mathematical Modelling and Numerical Analysis 37, no. 2 (2003): 319-338.
  - Chern, I-L, Liu, J-G, and Wang, W-C. "Accurate evaluation of electrostatics for macromolecules in solution." Methods and Applications of Analysis 10 (2003): 309-328. (Academic Article)
  - 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
  - Wang, C, and Liu, J-G. "Positivity property of second-order flux-splitting schemes for the compressible Euler equations." Discrete and Continuous Dynamical Systems - Series B 3, no. 2 (2003): 201-228.
  - Wang, C, and Liu, J-G. "Fourth order convergence of a compact difference solver for incompressible flow." Commun. Appl. Anal. 7 (2003): 171-191. (Academic Article)
  - Weinan, E, and Liu, J-G. "Gauge method for viscous incompressible flows." Comm. Math. Sci. 1 (2003): 317-332. (Academic Article)
  - Johnston, H, and Liu, J-G. "Finite Difference Schemes for Incompressible Flow Based on Local Pressure Boundary Conditions." Journal of Computational Physics 180, no. 1 (July 2002): 120-154. Full Text
  - Wang, C, and Liu, J-G. "Analysis of finite difference schemes for unsteady Navier-Stokes equations in vorticity formulation." Numerische Mathematik 91, no. 3 (2002): 543-576. Full Text
  - Weinan, E, and Liu, J-G. "Projection method III: Spatial discretization on the staggered grid." Mathematics of Computation 71, no. 237 (2002): 27-47. Full Text
  - Liu, J-G, and Wang, W-C. "An energy-preserving MAC-Yee scheme for the incompressible MHD equation." Journal of Computational Physics 174, no. 1 (2001): 12-37. Full Text
  - Liu, J-G, and Weinan, E. "Simple finite element method in vorticity formulation for incompressible flow." Math. Comp. 69 (2001): 1385-1407. (Academic Article)
  - Liu, J-G, and Weinan, E. "Simple finite element method in vorticity formulation for incompressible flows." Mathematics of Computation 70, no. 234 (2001): 579-593. Full Text
  - Liu, J-G, and Xin, Z. "Convergence of point vortex method for 2-D vortex sheet." Math. Comp. 70 (2001): 565-606. (Academic Article)
  - Liu, J-G, and Xin, Z. "Convergence of the point vortex method for 2-D vortex sheet." Mathematics of Computation 70, no. 234 (2001): 595-606. Full Text
  - Weinan, E, and Liu, JG. "Gauge finite element method for incompressible flows." International Journal for Numerical Methods in Fluids 34, no. 8 (December 1, 2000): 701-710. Full Text
  - Liu, J-G, and Shu, C-W. "A High-Order Discontinuous Galerkin Method for 2D Incompressible Flows." Journal of Computational Physics 160, no. 2 (May 2000): 577-596. Full Text
  - Liu, JG, and Xin, Z. "Convergence of a Galerkin method for 2-D discontinuous Euler flows." Communications on Pure and Applied Mathematics 53, no. 6 (January 1, 2000): 786-798. Full Text
  - Wang, C, and Liu, J-G. "Convergence of gauge method for incompressible flow." Mathematics of Computation 69, no. 232 (2000): 1385-1407.
  - Lefloch, PG, and Liu, J-G. "Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions." Mathematics of Computation 68, no. 227 (1999): 1025-1055.
  - Wang, ZJ, Liu, JG, and Childress, S. "Connection between corner vortices and shear layer instability in flow past an ellipse." Physics of Fluids 11, no. 9 (1999): 2446-2448.
  - Choi, H, and Liu, J-G. "The Reconstruction of Upwind Fluxes for Conservation Laws: Its Behavior in Dynamic and Steady State Calculations." Journal of Computational Physics 144, no. 2 (1998): 237-256. Full Text
  - Xu, E, and Liu, J-G. "Pricing of mortgage-backed securities with option-adjusted spread." Managerial Finance 24 (1998): 94-109. (Academic Article)
  - Chen, G-Q, and Liu, J-G. "Convergence of difference schemes with high resolution for conservation laws." Mathematics of Computation 66, no. 219 (1997): 1027-1053.
  - Weinan, E, and Liu, J-G. "Finite difference schemes for incompressible flows in the velocity - impulse density formulation." Journal of Computational Physics 130, no. 1 (1997): 67-76.
  - Weinan, E, and Liu, J-G. "Finite Difference Methods for 3D Viscous Incompressible Flows in the Vorticity-Vector Potential Formulation on Nonstaggered Grids." Journal of Computational Physics 138, no. 1 (1997): 57-82. Full Text
  - Jin, S, and Liu, J-G. "The effects of numerical viscosities: I. Slowly moving shocks." Journal of Computational Physics 126, no. 2 (1996): 373-389. Full Text
  - Jin, S, and Liu, J-G. "Oscillations induced by numerical viscosities." Mat. Contemp. 10 (1996): 169-180. (Academic Article)
  - Levermore, CD, and Liu, J-G. "Large oscillations arising in a dispersive numerical scheme." Physica D: Nonlinear Phenomena 99, no. 2-3 (1996): 191-216.
  - Liu, J-G, and Xin, Z. "Boundary layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation." Arch. Rat. Mech. Anal. 135 (1996): 61-105. (Academic Article)
  - Liu, J-G, and Xin, Z. "Kinetic and viscous boundary layers for broadwell equations." Transport Theory and Statistical Physics 25, no. 3-5 (1996): 447-461.
  - Weinan, E, and Liu, J-G. "Projection method II: Godunov-Ryabenki analysis." SIAM Journal on Numerical Analysis 33, no. 4 (1996): 1597-1621.
  - Weinan, E, and Liu, J-G. "Essentially compact schemes for unsteady viscous incompressible flows." Journal of Computational Physics 126, no. 1 (1996): 122-138. Full Text
  - Weinan, E, and Liu, J-G. "Vorticity boundary condition and related issues for finite difference schemes." Journal of Computational Physics 124, no. 2 (1996): 368-382. Full Text
  - Liu, J-G, and Xin, Z. "Convergence of vortex methods for weak solutions to the 2-D Euler equations with vortex sheets data." Comm. Pure Appl. Math. 48 (1995): 611-628. (Academic Article)
  - Weinan, E, and Liu, J-G. "Projection method I: convergence and numerical boundary layers." SIAM J. Numer. Anal. 32 (1995): 1017-1057. (Academic Article)
  - Jin, S, and Liu, J-G. "Relaxation and diffusion enhanced dispersive waves." Proceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences 446, no. 1928 (1994): 555-563.
  - Lefloch, P, and Liu, J-G. "Discrete entropy and monotonicity criteria for hyperbolic conservation laws." C.R. Acad. Sci. Paris. 319 (1994): 881-886. (Academic Article)
  - Chen, G-Q, and Liu, J-G. "Convergence of second-order schemes for isentropic gas dynamics." Math. Comp. 61 (1993): 607-629. (Academic Article)
  - Engquist, B, and Liu, J-G. "Numerical methods for oscillatory solutions to hyperbolic problems." Comm. Pure Appl. Math. 46 (1993): 1327-1361. (Academic Article)
  - Liu, J-G, and Xin, Z. "Nonlinear stability of discrete shocks for systems of conservation laws." Archive for Rational Mechanics and Analysis 125, no. 3 (1993): 217-256. Full Text
  - Liu, J-G, and Xin, Z. "L1-stability of stationary discrete shocks." Math. Comp. 60 (1993): 233-244. (Academic Article)
  - Huang, H, Liu, J-G, and Lu, J. "Learning interacting particle systems: diffusion parameter estimation for aggregation equations." Open Access Copy Link to Item
  - Huang, H, Liu, J-G, and Pickl, P. "On the mean-field limit for the Vlasov-Poisson-Fokker-Planck system." . Open Access Copy Link to Item
  - Liu, J-G, Lu, J, Margetis, D, and Marzuola, JL. "Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model." Open Access Copy Link to Item
Teaching & Mentoring
Recent Courses
Scholarly, Clinical, & Service Activities
Presentations & Appearances
Outreach & Engaged Scholarship
- Unknown. Promotion and tenure external evaluators for various universities. January 1, 2012 2012
Service to the Profession

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.

Education, Training, & Certifications

In the News

Global Scholarship

Teaching

Selected Grants

Selected Publications

Conference Papers

Journal Articles

Recent Courses

Presentations & Appearances

Outreach & Engaged Scholarship

Service to the Profession