JianGuo 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 277080320
 jianguo.liu@duke.edu (919) 6602500
 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
 Expertise

Global Scholarship

Teaching

 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 diffusiondrift many particle systems in probability under a sobolev norm." January 1, 2016. Full Text

Journal Articles
 Li, L, Liu, JG, and Lu, J. "Fractional Stochastic Differential Equations Satisfying FluctuationDissipation Theorem." Journal of Statistical Physics 169, no. 2 (October 2017): 316339. Full Text Open Access Copy
 Gao, Y, Ji, H, Liu, JG, and Witelski, TP. "Global existence of solutions to a tear film model with locally elevated evaporation rates." Physica D: Nonlinear Phenomena 350 (July 2017): 1325. Full Text
 Liu, JG, 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): 291313. Full Text
 Gao, Y, Liu, JG, 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): 873926. Full Text Open Access Copy
 Degond, P, Liu, JG, and Pego, RL. "Coagulation–Fragmentation Model for Animal GroupSize Statistics." Journal of Nonlinear Science 27, no. 2 (April 2017): 379424. Full Text
 Huang, H, and Liu, JG. "Error estimate of a random particle blob method for the KellerSegel equation." Mathematics of Computation 86, no. 308 (February 15, 2017): 27192744. Full Text
 Liu, JG, 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): 14611492. Full Text
 Degond, P, Herty, M, and Liu, JG. "Meanfield games and model predictive control." Communications in Mathematical Sciences 15, no. 5 (2017): 14031422. Full Text
 Degond, P, Liu, JG, MerinoAceituno, 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): 159182. Full Text
 Gao, Y, Liu, JG, and Lu, J. "Weak Solution of a Continuum Model For Vicinal Surface in The AttachmentDetachmentLimited Regime." SIAM Journal on Mathematical Analysis 49, no. 3 (January 2017): 17051731. Full Text Open Access Copy
 Gao, Y, and Liu, JG. "Global Convergence of a Sticky Particle Method for the Modified CamassaHolm Equation." SIAM Journal on Mathematical Analysis 49, no. 2 (January 2017): 12671294. Full Text
 Huang, H, and Liu, JG. "Discreteintime random particle blob method for the KellerSegel equation and convergence analysis." Communications in Mathematical Sciences 15, no. 7 (January 1, 2017): 18211842. Full Text
 Liu, JG, and Wang, J. "A generalized Sz. Nagy inequality in higher dimensions and the critical thin film equation." Nonlinearity 30, no. 1 (January 1, 2017): 3560. Full Text
 Liu, JG, 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): 22202245. Full Text
 Liu, JG, and Cong, W. "Uniform $L^{\infty}$ boundedness for a degenerate parabolicparabolic KellerSegel model." Discrete and Continuous Dynamical Systems  Series B 22, no. 2 (December 2016): 307338. Full Text
 Huang, H, and Liu, JG. "A note on Monge–Ampère Keller–Segel equation." Applied Mathematics Letters 61 (November 2016): 2634. Full Text
 Huang, H, and Liu, JG. "Error estimates of the aggregationdiffusion splitting algorithms for the KellerSegel equations." Discrete and Continuous Dynamical Systems  Series B 21, no. 10 (November 2016): 34633478. Full Text
 Liu, JG, and Cong, W. "A degenerate $p$Laplacian KellerSegel model." Kinetic and Related Models 9, no. 4 (September 2016): 687714. Full Text
 Liu, JG, and Huang, H. "Wellposedness for the KellerSegel equation with fractional Laplacian and the theory of propagation of chaos." Kinetic and Related Models 9, no. 4 (September 2016): 715748. Full Text
 Herschlag, G, Liu, JG, and Layton, AT. "Fluid extraction across pumping and permeable walls in the viscous limit." Physics of Fluids 28, no. 4 (April 2016): 041902041902. Full Text
 Liu, JG, and Wang, J. "A Note on L ∞ $L^{\infty}$ Bound and Uniqueness to a Degenerate KellerSegel Model." Acta Applicandae Mathematicae 142, no. 1 (April 2016): 173188. Full Text
 Liu, JG, and Pego, RL. "On generating functions of Hausdorff moment sequences." Transactions of the American Mathematical Society 368, no. 12 (February 2, 2016): 84998518. Full Text
 Chen, J, Liu, JG, and Zhou, Z. "On a SchrödingerLandauLifshitz System: Variational Structure and Numerical Methods." Multiscale Modeling & Simulation 14, no. 4 (January 2016): 14631487. Full Text
 Liu, JG, and Xu, X. "Existence Theorems for a Multidimensional Crystal Surface Model." SIAM Journal on Mathematical Analysis 48, no. 6 (January 2016): 36673687. Full Text
 Xue, Y, Wang, C, and Liu, JG. "Simple Finite Element Numerical Simulation of Incompressible Flow Over Nonrectangular Domains and the SuperConvergence Analysis." Journal of Scientific Computing 65, no. 3 (December 2015): 11891216. Full Text
 Chertock, A, Liu, JG, and Pendleton, T. "Elastic collisions among peakon solutions for the Camassa–Holm equation." Applied Numerical Mathematics 93 (July 2015): 3046. Full Text
 Degond, P, Frouvelle, A, and Liu, JG. "Phase Transitions, Hysteresis, and Hyperbolicity for SelfOrganized Alignment Dynamics." Archive for Rational Mechanics and Analysis 216, no. 1 (April 2015): 63115. 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): 032403. Full Text Open Access Copy
 Chertock, A, Liu, JG, and Pendleton, T. "Elastic collisions among peakon solutions for the CamassaHolm equation." Applied Numerical Mathematics 93 (January 1, 2015): 3046. Full Text
 Degond, P, Frouvelle, A, and Liu, JG. "Phase Transitions, Hysteresis, and Hyperbolicity for SelfOrganized Alignment Dynamics." Archive for Rational Mechanics and Analysis 216, no. 1 (January 1, 2015): 63115. Full Text
 Herschlag, G, Liu, JG, 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): 22462267. Full Text
 Coquel, F, Jin, S, Liu, JG, and Wang, L. "WellPosedness and Singular Limit of a Semilinear Hyperbolic Relaxation System with a TwoScale Discontinuous Relaxation Rate." Archive for Rational Mechanics and Analysis 214, no. 3 (December 2014): 10511084. Full Text
 Degond, P, Liu, JG, and Ringhofer, C. "Evolution of wealth in a nonconservative economy driven by local Nash equilibria." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2028 (October 6, 2014): 2013039420130394. Full Text
 Johnston, H, Wang, C, and Liu, JG. "A Local Pressure Boundary Condition Spectral Collocation Scheme for the ThreeDimensional Navier–Stokes Equations." Journal of Scientific Computing 60, no. 3 (September 2014): 612626. Full Text
 Goudon, T, Jin, S, Liu, JG, and Yan, B. "Asymptoticpreserving schemes for kineticfluid modeling of disperse twophase flows with variable fluid density." International Journal for Numerical Methods in Fluids 75, no. 2 (May 20, 2014): 81102. Full Text
 Goudon, T, Jin, S, Liu, JG, and Yan, B. "Asymptoticpreserving schemes for kineticfluid modeling of disperse twophase flows with variable fluid density." International Journal for Numerical Methods in Fluids 75, no. 2 (May 20, 2014): 81102. Full Text
 Duan, Y, and Liu, JG. "Convergence analysis of the vortex blob method for the bequation." Discrete and Continuous Dynamical Systems Series A 34, no. 5 (May 1, 2014): 19952011. 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): 751780. Full Text
 Chae, D, Degond, P, and Liu, JG. "Wellposedness for hallmagnetohydrodynamics." Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire 31, no. 3 (January 1, 2014): 555565. Full Text
 Chen, X, Jüngel, A, and Liu, JG. "A note on AubinLionsDubinskiǐ Lemmas." Acta Applicandae Mathematicae 133, no. 1 (January 1, 2014): 3343. Full Text
 Chen, X, Li, X, and Liu, JG. "Existence and uniqueness of global weak solution to a kinetic model for the sedimentation of rodlike particles." Communications in Mathematical Sciences 12, no. 8 (2014): 15791601. Full Text
 Coquel, F, Jin, S, Liu, JG, and Wang, L. "WellPosedness and Singular Limit of a Semilinear Hyperbolic Relaxation System with a TwoScale Discontinuous Relaxation Rate." Archive for Rational Mechanics and Analysis 214, no. 3 (January 1, 2014): 10511084. Full Text
 Degond, P, Herty, M, and Liu, JG. "Flow on Sweeping Networks." Multiscale Modeling & Simulation 12, no. 2 (January 2014): 538565. Full Text
 Degond, P, Liu, JG, and Ringhofer, C. "Largescale dynamics of meanfield games driven by local nash equilibria." Journal of Nonlinear Science 24, no. 1 (January 1, 2014): 93115. Full Text
 Johnston, H, Wang, C, and Liu, JG. "A Local Pressure Boundary Condition Spectral Collocation Scheme for the ThreeDimensional Navier–Stokes Equations." Journal of Scientific Computing 60, no. 3 (2014): 612626. Full Text
 Zou, C, Liu, JG, and Bian, S. "Ultracontractivity for KellerSegel model with diffusion exponent $m>12/d$." Kinetic and Related Models 7, no. 1 (December 2013): 928. 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 MultiDimensional KellerSegel Model with Diffusion Exponent m > 0." Communications in Mathematical Physics (2013): 154. Full Text
 Bian, S, and Liu, JG. "Dynamic and Steady States for MultiDimensional KellerSegel Model with Diffusion Exponent m > 0." Communications in Mathematical Physics 323, no. 3 (2013): 10171070. Full Text
 Chae, D, Degond, P, and Liu, JG. "Wellposedness for Hallmagnetohydrodynamics." Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis (2013). Full Text
 Chen, X, Jüngel, A, and Liu, JG. "A Note on AubinLionsDubinskiǐ Lemmas." Acta Applicandae Mathematicae (2013): 111.
 Chen, X, and Liu, JG. "Global weak entropy solution to DoiSaintillanShelley model for active and passive rodlike and ellipsoidal particle suspensions." Journal of Differential Equations 254, no. 7 (2013): 27642802. Full Text
 Chen, X, and Liu, JG. "Analysis of polymeric flow models and related compactness theorems in weighted spaces." SIAM Journal on Mathematical Analysis 45, no. 3 (2013): 11791215. Full Text
 Degond, P, Frouvelle, A, and Liu, JG. "Macroscopic limits and phase transition in a system of selfpropelled particles." Journal of Nonlinear Science 23, no. 3 (2013): 427456. 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 (2013): 130.
 Degond, P, Liu, JG, and Ringhofer, C. "LargeScale Dynamics of MeanField Games Driven by Local Nash Equilibria." Journal of Nonlinear Science (2013): 123. Full Text
 Goudon, T, Jin, S, Liu, JG, and Yan, B. "Asymptoticpreserving schemes for kineticfluid modeling of disperse twophase flows." Journal of Computational Physics 246 (2013): 145164. Full Text
 Carrillo, JA, Chen, L, Liu, JG, and Wang, J. "A note on the subcritical two dimensional KellerSegel system." Acta Applicandae Mathematicae 119, no. 1 (2012): 4355. Full Text
 Chae, D, and Liu, JG. "Blowup, Zero α Limit and the Liouville Type Theorem for the EulerPoincaré Equations." Communications in Mathematical Physics 314, no. 3 (2012): 671687. Full Text
 Chen, L, Liu, JG, and Wang, J. "Multidimensional degenerate KellerSegel system with critical diffusion exponent 2n/(n + 2)." SIAM Journal on Mathematical Analysis 44, no. 2 (2012): 10771102. Full Text
 Chen, X, and Liu, JG. "Two nonlinear compactness theorems in L ^{p}(0,T;B)." Applied Mathematics Letters 25, no. 12 (2012): 22522257. Full Text
 Chertock, A, Liu, JG, 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): 121. Full Text
 Degond, P, Frouvelle, A, and Liu, JG. "Macroscopic Limits and Phase Transition in a System of Selfpropelled Particles." Journal of Nonlinear Science (2012): 130. Full Text
 Degond, P, and Liu, JG. "Hydrodynamics of selfalignment interactions with precession and derivation of the LandauLifschitzGilbert equation." Mathematical Models and Methods in Applied Sciences 22, no. SUPPL.1 (2012). Full Text
 Frouvelle, A, and Liu, JG. "Dynamics in a kinetic model of oriented particles with phase transition." SIAM Journal on Mathematical Analysis 44, no. 2 (2012): 791826. Full Text
 Haack, J, Jin, S, and Liu, JG. "An allspeed asymptoticpreserving method for the isentropic Euler and NavierStokes equations." Communications in Computational Physics 12, no. 4 (2012): 955980. Full Text
 Qin, HB, Wang, YG, Zhang, HB, Liu, J, and Zhuo, Z. "A passively modelocked Nd:YVO _{4} Laser with a carbon nanotube saturable absorber." Laser Physics 22, no. 4 (2012): 684687. Full Text
 Acheritogaray, M, Degond, P, Frouvelle, A, and Liu, JG. "Kinetic formulation and global existence for the hallmagnetohydrodynamics system." Kinetic and Related Models 4, no. 4 (2011): 901918. Full Text
 Huang, YL, Liu, JG, and Wang, WC. "An FFT based fast poisson solver on spherical shells." Communications in Computational Physics 9, no. 3 (2011): 649667. Full Text
 Jin, S, Liu, JG, and Wang, L. "A domain decomposition method for semilinear hyperbolic systems with twoscale relaxations (Accepted)." Math. Comp. (2011). (Academic Article)
 Liu, JG, and Lorz, A. "A coupled chemotaxisfluid model: Global existence." Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis 28, no. 5 (2011): 643652. Full Text
 Simsek, E, Liu, J, and Liu, QH. "A spectral integral method for the analysis of nano wires." 2011 30th URSI General Assembly and Scientific Symposium, URSIGASS 2011 (2011). Full Text
 Zheng, W, Gao, H, Liu, JG, Zhang, Y, Ye, Q, and Swank, C. "General solution to gradientinduced transverse and longitudinal relaxation of spins undergoing restricted diffusion." Physical Review A  Atomic, Molecular, and Optical Physics 84, no. 5 (2011). Full Text
 Liu, JG, Liu, J, and Pego, RL. "Stable and accurate pressure approximation for unsteady incompressible viscous flow." Journal of Computational Physics 229, no. 9 (2010): 34283453. Full Text
 Liu, JG, 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): 14741491. Full Text Open Access Copy
 Liu, JG, and Pego, R. "Stable discretization of magnetohydrodynamics in bounded domains." Commun. Math. Sci. 8 (2010): 234251. (Academic Article)
 Liu, JG, and Pego, RL. "Stable discretization of magnetohydrodynamics in bounded domains." Communications in Mathematical Sciences 8, no. 1 (2010): 235251.
 Ha, SY, and Liu, JG. "A simple proof of the CuckerSmale flocking dynamics and meanfield limit." Communications in Mathematical Sciences 7, no. 2 (2009): 297325.
 Lin, Y, Lee, JH, Liu, J, Chai, M, Mix, JA, and Liu, QH. "A hybrid SIMSEM method for 3D electromagnetic scattering problems." IEEE Transactions on Antennas and Propagation 57, no. 11 (2009): 36553663. Full Text
 Liu, JG, Liu, J, and Pego, RL. "Error estimates for finiteelement NavierStokes solvers without standard InfSup conditions." Chinese Annals of Mathematics. Series B 30, no. 6 (2009): 743768. Full Text
 Liu, JG, and Wang, WC. "Characterization and regularity for axisymmetric solenoidal vector fields with application to navierstokes equation." SIAM Journal on Mathematical Analysis 41, no. 5 (2009): 18251850. Full Text
 Liu, QH, Lin, Y, Liu, J, Lee, JH, and Şimşek, E. "A 3D spectral integral method (SIM) for surface integral equations." IEEE Microwave and Wireless Components Letters 19, no. 2 (2009): 6264. Full Text
 Degond, P, Liu, JG, and Vignal, MH. "Analysis of an asymptotic preserving scheme for the EulerPoisson system in the quasineutral limit." SIAM Journal on Numerical Analysis 46, no. 3 (2008): 12981322. Full Text
 Hsia, CH, Liu, JG, and Wang, C. "Structural stability and bifurcation for 2D incompressible ows with symmetry." Meth. Appl. Anal. 15 (2008): 495512. (Academic Article)
 Lin, P, Liu, JG, and Lu, X. "Long time numerical solution of the NavierStokes equations based on a sequential regularization formulation." SIAM Journal on Scientific Computing 31, no. 1 (2008): 398419. Full Text
 Liu, JG, and Wang, C. "A fourth order numerical method for the primtive equations formulated in mean vorticity." Communications in Computational Physics 4, no. 1 (2008): 2655.
 Lu, X, Lin, P, and Liu, JG. "Analysis of a sequential regularization method for the unsteady NavierStokes equations." Mathematics of Computation 77, no. 263 (2008): 14671494. Full Text
 Antman, SS, and Liu, JG. "Basic themes and pretty problems of nonlinear solid mechanics." Milan Journal of Mathematics 75, no. 1 (2007): 135176. Full Text
 Degond, P, Jin, S, and Liu, JG. "Machnumber uniform asymptotic preserving Gauge schemes for compressible flows." Bulletin of the Institute of Mathematics Academia Sinica (New Series) 2 (2007): 851892. (Academic Article)
 Liu, J, Lin, Y, Lee, JH, Simsek, E, and Liu, QH. "Application of the hybrid spectral integral method with spectral element method." IEEE Antennas and Propagation Society, APS International Symposium (Digest) (2007): 5611. Full Text
 Liu, J, and Liu, QH. "A novel radiation boundary condition for finiteelement method." Microwave and Optical Technology Letters 49, no. 8 (2007): 19952002. Full Text
 Liu, JG, Liu, J, and Pego, R. "Stability and convergence of efficient NavierStokes solvers via a commutator estimate via a commutator estimate." Comm. Pure Appl. Math. 60 (2007): 14431487. (Academic Article)
 Liu, JG, Liu, J, and Pego, RL. "Stability and convergence of efficient NavierStokes solvers via a commutator estimate." Communications on Pure and Applied Mathematics 60, no. 10 (2007): 14431487. Full Text
 Moore, J, Cheng, Z, Hao, J, Guo, G, Liu, JG, Lin, C, and Yu, L. "Effects of solidstate 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): 1017310182. Full Text
 Degond, P, Liu, JG, and Mieussens, L. "Macroscopic fluid models with localized kinetic upscaling effects." Multiscale Modeling and Simulation 5, no. 3 (2006): 940979. Full Text
 Liu, JG, Samelson, R, and Wang, C. "Global weak solution of planetary geostrophic equations with inviscid geostrophic balance." Applicable Analysis 85 (2006): 593605. (Academic Article)
 Liu, JG, and Wang, WC. "Convergence analysis of the energy and helicity preserving scheme for axisymmetric flows." SIAM Journal on Numerical Analysis 44, no. 6 (2006): 24562480. Full Text
 Moore, J, Liu, JG, 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): 53135322. Full Text
 Şimşek, E, Liu, J, and Liu, QH. "A spectral integral method and hybrid SIM/FEM for layered media." IEEE Transactions on Microwave Theory and Techniques 54, no. 11 (2006): 38783884. Full Text
 Simsek, E, Liu, J, and Liu, QH. "A spectral integral method for layered media." IEEE Antennas and Propagation Society, APS International Symposium (Digest) 3 B (2005): 238. Full Text
 Ghil, M, Liu, JG, Wang, C, and Wang, S. "Boundarylayer separation and adverse pressure gradient for 2D viscous incompressible flow." Physica D: Nonlinear Phenomena 197, no. 12 (2004): 149173. Full Text
 Johnston, H, and Liu, JG. "Accurate, stable and efficient NavierStokes solvers based on explicit treatment of the pressure term." Journal of Computational Physics 199, no. 1 (2004): 221259. Full Text
 Li, B, and Liu, JG. "Eptaxial growth without slope selection: energetics, coarsening, and dynamic scaling." J. Nonlinear Sci. 14 (2004): 429451. (Academic Article)
 Li, B, and Liu, JG. "Epitaxial growth without slope selection: Energetics, coarsening, and dynamic scaling." Journal of Nonlinear Science 14, no. 5 (2004): 429451. Full Text
 Lin, HE, Liu, JG, and Xu, WQ. "Effects of small viscosity and far field boundary conditions for hyperbolic systems." Communications on Pure and Applied Analysis 3, no. 2 (2004): 267290.
 Liu, J, and Liu, QH. "A Spectral Integral Method (SIM) for Periodic and Nonperiodic Structures." IEEE Microwave and Wireless Components Letters 14, no. 3 (2004): 9799. Full Text
 Liu, J, and Liu, QH. "A spectral integral method for periodic and nonperiodic structures." IEEE Antennas and Propagation Society, APS International Symposium (Digest) 4 (2004): 38753878.
 Liu, JG, and Wang, C. "High order finite difference method for unsteady incompressible flow on multiconnected domain in vorticitystream function formulation." Computer and Fluids 33 (2004): 223255. (Academic Article)
 Liu, JG, and Wang, C. "High order finite difference methods for unsteady incompressible flows in multiconnected domains." Computers and Fluids 33, no. 2 (2004): 223255. Full Text
 Liu, JG, and Wang, WC. "Energy and helicity preserving schemes for hydro and magnetohydrodynamics flows with symmetry." Journal of Computational Physics 200, no. 1 (2004): 833. Full Text
 Liu, JG, and Xu, WQ. "Far field boundary condition for convection diffusion equation at zero viscosity limit." Quarterly of Applied Mathematics 62, no. 1 (2004): 2752.
 Wang, C, Liu, JG, and Johnston, H. "Analysis of a fourth order finite difference method for the incompressible Boussinesq equations." Numerische Mathematik 97, no. 3 (2004): 555594. Full Text
 ChainaisHillairet, C, Liu, JG, and Peng, YJ. "Finite volume scheme for multidimensional driftdiffusion equations and convergence analysis." Mathematical Modelling and Numerical Analysis 37, no. 2 (2003): 319338.
 Chern, IL, Liu, JG, and Wang, WC. "Accurate evaluation of electrostatics for macromolecules in solution." Methods and Applications of Analysis 10 (2003): 309328. (Academic Article)
 Duraisamy, K, Baeder, JD, and Liu, JG. "Concepts and Application of TimeLimiters to High Resolution Schemes." Journal of Scientific Computing 19, no. 13 (2003): 139162. Full Text
 Li, B, and Liu, JG. "Thin film epitaxy with or without slope selection." European Journal of Applied Mathematics 14, no. 6 (2003): 713743. Full Text
 Liu, JG, Wang, C, and Johnston, H. "A Fourth Order Scheme for Incompressible Boussinesq Equations." Journal of Scientific Computing 18, no. 2 (2003): 253285. Full Text
 Wang, C, and Liu, JG. "Positivity property of secondorder fluxsplitting schemes for the compressible Euler equations." Discrete and Continuous Dynamical Systems  Series B 3, no. 2 (2003): 201228.
 Wang, C, and Liu, JG. "Fourth order convergence of a compact difference solver for incompressible flow." Commun. Appl. Anal. 7 (2003): 171191. (Academic Article)
 Weinan, E, and Liu, JG. "Gauge method for viscous incompressible flows." Comm. Math. Sci. 1 (2003): 317332. (Academic Article)
 Johnston, H, and Liu, JG. "Finite difference schemes for incompressible flow based on local pressure boundary conditions." Journal of Computational Physics 180, no. 1 (2002): 120154. Full Text
 Wang, C, and Liu, JG. "Analysis of finite difference schemes for unsteady NavierStokes equations in vorticity formulation." Numerische Mathematik 91, no. 3 (2002): 543576. Full Text
 Weinan, E, and Liu, JG. "Projection method III: Spatial discretization on the staggered grid." Mathematics of Computation 71, no. 237 (2002): 2747. Full Text
 Liu, JG, and Wang, WC. "An energypreserving MACYee scheme for the incompressible MHD equation." Journal of Computational Physics 174, no. 1 (2001): 1237. Full Text
 Liu, JG, and Weinan, E. "Simple finite element method in vorticity formulation for incompressible flow." Math. Comp. 69 (2001): 13851407. (Academic Article)
 Liu, JG, and Weinan, E. "Simple finite element method in vorticity formulation for incompressible flows." Mathematics of Computation 70, no. 234 (2001): 579593. Full Text
 Liu, JG, and Xin, Z. "Convergence of point vortex method for 2D vortex sheet." Math. Comp. 70 (2001): 565606. (Academic Article)
 Liu, JG, and Xin, Z. "Convergence of the point vortex method for 2D vortex sheet." Mathematics of Computation 70, no. 234 (2001): 595606. Full Text
 Liu, JG, and Shu, CW. "A HighOrder Discontinuous Galerkin Method for 2D Incompressible Flows." Journal of Computational Physics 160, no. 2 (2000): 577596. Full Text
 Liu, JG, and Xin, Z. "Convergence of a Galerkin method for 2D discontinuous Euler flows." Communications on Pure and Applied Mathematics 53, no. 6 (2000): 786798.
 Wang, C, and Liu, JG. "Convergence of gauge method for incompressible flow." Mathematics of Computation 69, no. 232 (2000): 13851407.
 Weinan, E, and Liu, JG. "Gauge finite element method for incompressible flows." International Journal for Numerical Methods in Fluids 34, no. 8 (2000): 701710. Full Text
 Lefloch, PG, and Liu, JG. "Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions." Mathematics of Computation 68, no. 227 (1999): 10251055.
 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): 24462448.
 Choi, H, and Liu, JG. "The Reconstruction of Upwind Fluxes for Conservation Laws: Its Behavior in Dynamic and Steady State Calculations." Journal of Computational Physics 144, no. 2 (1998): 237256. Full Text
 Xu, E, and Liu, JG. "Pricing of mortgagebacked securities with optionadjusted spread." Managerial Finance 24 (1998): 94109. (Academic Article)
 Chen, GQ, and Liu, JG. "Convergence of difference schemes with high resolution for conservation laws." Mathematics of Computation 66, no. 219 (1997): 10271053.
 Weinan, E, and Liu, JG. "Finite difference schemes for incompressible flows in the velocity  impulse density formulation." Journal of Computational Physics 130, no. 1 (1997): 6776.
 Weinan, E, and Liu, JG. "Finite Difference Methods for 3D Viscous Incompressible Flows in the VorticityVector Potential Formulation on Nonstaggered Grids." Journal of Computational Physics 138, no. 1 (1997): 5782. Full Text
 Jin, S, and Liu, JG. "The effects of numerical viscosities: I. Slowly moving shocks." Journal of Computational Physics 126, no. 2 (1996): 373389. Full Text
 Jin, S, and Liu, JG. "Oscillations induced by numerical viscosities." Mat. Contemp. 10 (1996): 169180. (Academic Article)
 Levermore, CD, and Liu, JG. "Large oscillations arising in a dispersive numerical scheme." Physica D: Nonlinear Phenomena 99, no. 23 (1996): 191216.
 Liu, JG, and Xin, Z. "Boundary layer behavior in the fluiddynamic limit for a nonlinear model Boltzmann equation." Arch. Rat. Mech. Anal. 135 (1996): 61105. (Academic Article)
 Liu, JG, and Xin, Z. "Kinetic and viscous boundary layers for broadwell equations." Transport Theory and Statistical Physics 25, no. 35 (1996): 447461.
 Weinan, E, and Liu, JG. "Projection method II: GodunovRyabenki analysis." SIAM Journal on Numerical Analysis 33, no. 4 (1996): 15971621.
 Weinan, E, and Liu, JG. "Essentially compact schemes for unsteady viscous incompressible flows." Journal of Computational Physics 126, no. 1 (1996): 122138. Full Text
 Weinan, E, and Liu, JG. "Vorticity boundary condition and related issues for finite difference schemes." Journal of Computational Physics 124, no. 2 (1996): 368382. Full Text
 Liu, JG, and Xin, Z. "Convergence of vortex methods for weak solutions to the 2D Euler equations with vortex sheets data." Comm. Pure Appl. Math. 48 (1995): 611628. (Academic Article)
 Weinan, E, and Liu, JG. "Projection method I: convergence and numerical boundary layers." SIAM J. Numer. Anal. 32 (1995): 10171057. (Academic Article)
 Jin, S, and Liu, JG. "Relaxation and diffusion enhanced dispersive waves." Proceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences 446, no. 1928 (1994): 555563.
 Lefloch, P, and Liu, JG. "Discrete entropy and monotonicity criteria for hyperbolic conservation laws." C.R. Acad. Sci. Paris. 319 (1994): 881886. (Academic Article)
 Chen, GQ, and Liu, JG. "Convergence of secondorder schemes for isentropic gas dynamics." Math. Comp. 61 (1993): 607629. (Academic Article)
 Engquist, B, and Liu, JG. "Numerical methods for oscillatory solutions to hyperbolic problems." Comm. Pure Appl. Math. 46 (1993): 13271361. (Academic Article)
 Liu, JG, and Xin, Z. "Nonlinear stability of discrete shocks for systems of conservation laws." Archive for Rational Mechanics and Analysis 125, no. 3 (1993): 217256. Full Text
 Liu, JG, and Xin, Z. "L1stability of stationary discrete shocks." Math. Comp. 60 (1993): 233244. (Academic Article)

 Teaching & Mentoring

Recent Courses
 MATH 557: Introduction to Partial Differential Equations 2017
 MATH 563: Applied Computational Analysis 2017
 MATH 575: Mathematical Fluid Dynamics 2017
 MATH 577: Mathematical Modeling 2017
 PHYSICS 137SK: Energy in the 21st Century and Beyond 2017
 PHYSICS 814: Introduction to Fluid Mechanics 2017
 COMPSCI 393: Research Independent Study 2016
 MATH 381K: Intermediate Mathematical Finance 2016
 Scholarly, Clinical, & Service Activities

Presentations & Appearances
 CoagulationFragmentation model without detailed balance for animal groupsize statistics. September 11, 2013 2013
 CoagulationFragmentation model without detailed balance for animal groupsize statistics. August 8, 2013 2013
 Phase transitions, hysteresis, and hyperbolicity for selforganized alignment dynamics. August 1, 2013 2013
 The dynamic and steady states for multidimensional KellerSegel model with the diffusion exponent m > 0. July 26, 2013 2013
 Phase transitions, hysteresis, and hyperbolicity for selforganized alignment dynamics. July 15, 2013 2013
 Phase transitions, hysteresis, and hyperbolicity for selforganized 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 multidimensional KellerSegel model with the diffusion exponent m>0. February 21, 2013 2013
 Phase transitions for selforganized dynamics and sweeping networks. January 1, 2013 2013
 Estimate on LaplaceLeray commutator and application to the NavierStokes 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 selfalignment in flocking dynamics. September 7, 2012 2012
 Multidimensional KellerSegel model with supercritical diffusion exponent. August 7, 2012 2012
 Multidimensional KellerSegel 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
 AsymptoticPreserving schemes for kinetic–fluid modeling of disperse twophase 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 selfalignment interactions. August 2, 2011 2011
 Multidimensional degenerate KellerSegel system with critical diffusion exponent 2n/(n+2). August 1, 2011 2011
 Hydrodynamics of selfalignment interactions with precession and derivation of the LandauLifschitzGilbert 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
 Asymptoticpreserving 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 selfpropelled 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 NavierStokes equation in bounded domain. November 12, 2010 2010
 Modeling and analysis of collective behavior of selfpropelled agents. November 11, 2010 2010
 Dynamics of orientational alignment and phase transition. November 1, 2010 2010
 Modeling and analysis of collective behavior of selfpropelled agents. October 19, 2010 2010
 Dynamics of orientational alignment and phase transition. October 1, 2010 2010
 Analysis of dynamics of DoiOnsager phase transition. September 29, 2010 2010
 Analysis of Dynamics of DoiOnsager Phase Transition. September 6, 2010 2010
 Estimate on commutator of the Laplacian and Leray projection operators and application to NavierStokes equation in bounded domain. September 3, 2010 2010
 Asymptoticpreserving schemes for some kinetic equations. August 31, 2010 2010
 Some estimates on collective behavior of selfpropelled biological agents. December 3, 2009 2009
 Asymptoticpreserving schemes for fluids equations and kinetic equations. November 17, 2009 2009
 Modeling and analysis of collective behavior of selfpropelled 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 selfpropelled agents. September 4, 2009 2009
 Controlling numerical dissipation and time stepping in some multiscale kinetic/fluid simulations. September 1, 2009 2009
 Modeling and analysis of collective behavior of selfpropelled agents. August 19, 2009 2009
 Some numerical analysis issues in material and fluids simulations. August 1, 2009 2009
 A simple proof of the CuckerSmale flocking dynamics and meanfield limit. July 1, 2009 2009
 A simple proof of the CuckerSmale flocking dynamics and meanfield limit. July 1, 2009 2009
 Asymptoticpreserving 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 NavierStokes 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 asymptoticpreserving schemes for compressible flows. August 1, 2008 2008
 A simple proof of CuckerSmale flocking dynamics and the mean field limit. July 25, 2008 2008
 A simple proof of CuckerSmale 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 CuckerSmale flocking dynamics and meanfield 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 CuckerSmale 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 NavierStokes solvers based on an unconstrained reformulation. March 4, 2008 2008
 Finite element NavierStokes solvers based on an unconstrained reformulation. February 22, 2008 2008

Outreach & Engaged Scholarship

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