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: Kinetic Models of Aggregation and Dispersion awarded by National Science Foundation 2015 - 2018
- 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
  - 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
  - Li, L, and Liu, JG. "p-Euler equations and p-Navier-Stokes equations (Accepted)." Journal of Differential Equations (January 1, 2018). Full Text
  - 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
  - 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
  - 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 (2017): 1-1. 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, 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, Wang, L, and Zhou, Z. "Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations." Mathematics of Computation (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, JG, 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). 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
  - 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, 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
  - 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 323, no. 3 (2013): 1017-1070. Full Text
  - Chae, D, Degond, P, and Liu, J-G. "Well-posedness for Hall-magnetohydrodynamics." Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis (2013). 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
  - 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 (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
  - Haack, J, Jin, S, and Liu, J-G. "An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equations." Communications in Computational Physics 12, no. 4 (2012): 955-980. 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 (2011): 901-918. 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)
  - Liu, J-G, and Lorz, A. "A coupled chemotaxis-fluid model: Global existence." Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis 28, no. 5 (2011): 643-652. Full Text
  - 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 (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 (2010): 1474-1491. Full Text
  - 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.
  - 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
  - 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)
  - 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 (2007): 1443-1487. Full Text
  - 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
  - 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
  - Moore, J, Liu, J-G, Zhou, K, and Yu, L. "Effects of genotype and environment on the antioxidant properties of hard winter wheat bran." Journal of Agricultural and Food Chemistry 54, no. 15 (2006): 5313-5322. 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
  - 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 (2004): 221-259. 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)
  - Li, B, and Liu, J-G. "Epitaxial growth without slope selection: Energetics, coarsening, and dynamic scaling." Journal of Nonlinear Science 14, no. 5 (2004): 429-451. Full Text
  - 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
  - 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
  - Li, B, and Liu, J-G. "Thin film epitaxy with or without slope selection." European Journal of Applied Mathematics 14, no. 6 (2003): 713-743. Full Text
  - Liu, J-G, Wang, C, and Johnston, H. "A Fourth Order Scheme for Incompressible Boussinesq Equations." Journal of Scientific Computing 18, no. 2 (2003): 253-285. 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 (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
  - Liu, J-G, and Shu, C-W. "A High-Order Discontinuous Galerkin Method for 2D Incompressible Flows." Journal of Computational Physics 160, no. 2 (2000): 577-596. Full Text
  - Liu, J-G, and Xin, Z. "Convergence of a Galerkin method for 2-D discontinuous Euler flows." Communications on Pure and Applied Mathematics 53, no. 6 (2000): 786-798.
  - Wang, C, and Liu, J-G. "Convergence of gauge method for incompressible flow." Mathematics of Computation 69, no. 232 (2000): 1385-1407.
  - Weinan, E, and Liu, J-G. "Gauge finite element method for incompressible flows." International Journal for Numerical Methods in Fluids 34, no. 8 (2000): 701-710. Full Text
  - 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
  - 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
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