Math @ Duke

Books
 Multiscale phenomena in complex fluids, Modeling, Analysis and Numerical Simulations, edited by T. Hou, C. Liu and J.G. Liu
(2009), World Scientific, ISBN 9789814273251
 Hyperbolic Problems: Theory, Numerics and Applications, volume I: Plenary & Invited Talks; volume II: Contributed Talks, Proceedings of Symposia in Applied Mathematics, edited by E. Tadmor, J.G. Liu, and A.E. Tzavaras, vol. 67
(2009), American Mathematical Society, ISBN 9780821847282
 Dynamics in Models of Coarsening, Coagulation, Condensation and Quantization, edited by W. Bao and J.G. Liu
(2007), World Scientific, ISBN 9789812708502
Papers Published
 Liu, JG; Lu, J; Margetis, D; Marzuola, JL, Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model,
Physica D: Nonlinear Phenomena, vol. 393
(June, 2019),
pp. 5467 [doi] [abs]
 Lafata, KJ; Hong, JC; Geng, R; Ackerson, BG; Liu, JG; Zhou, Z; Torok, J; Kelsey, CR; Yin, FF, Association of pretreatment radiomic features with lung cancer recurrence following stereotactic body radiation therapy.,
Phys Med Biol, vol. 64 no. 2
(January, 2019),
pp. 025007 [doi] [abs]
 Huang, H; Liu, JG; Lu, J, Learning interacting particle systems: Diffusion parameter estimation for aggregation equations,
Mathematical Models and Methods in Applied Sciences, vol. 29 no. 1
(January, 2019),
pp. 129 [doi] [abs]
 Gao, Y; Ji, H; Liu, JG; Witelski, TP, A vicinal surface model for epitaxial growth with logarithmic free energy,
Discrete and Continuous Dynamical Systems Series B, vol. 23 no. 10
(December, 2018),
pp. 44334453, American Institute of Mathematical Sciences (AIMS) [doi] [abs]
 Feng, Y; Li, L; Liu, JG; Xu, X, Continuous and discrete one dimensional autonomous fractional odes,
Discrete and Continuous Dynamical Systems Series B, vol. 23 no. 8
(October, 2018),
pp. 31093135, American Institute of Mathematical Sciences (AIMS) [doi] [abs]
 Feng, Y; Li, L; Liu, JG; Xu, X, A note on onedimensional time fractional ODEs,
Applied Mathematics Letters, vol. 83
(September, 2018),
pp. 8794, Elsevier BV [doi] [abs]
 Li, L; Liu, JG; Wang, L, Cauchy problems for Keller–Segel type time–space fractional diffusion equation,
Journal of Differential Equations, vol. 265 no. 3
(August, 2018),
pp. 10441096, Elsevier BV [doi] [abs]
 Liu, JG; Tang, M; Wang, L; Zhou, Z, An accurate front capturing scheme for tumor growth models with a free boundary limit,
Journal of Computational Physics, vol. 364
(July, 2018),
pp. 7394, Elsevier BV [doi] [abs]
 Chen, K; Li, Q; Liu, JG, Online learning in optical tomography: A stochastic approach,
Inverse Problems, vol. 34 no. 7
(May, 2018),
pp. 075010075010, IOP Publishing [doi] [abs]
 Liu, JG; Xu, X, Partial regularity of weak solutions to a PDE system with cubic nonlinearity,
Journal of Differential Equations, vol. 264 no. 8
(April, 2018),
pp. 54895526, ACADEMIC PRESS INC ELSEVIER SCIENCE [doi] [abs]
 Li, L; Liu, JG, pEuler equations and pNavier–Stokes equations,
Journal of Differential Equations, vol. 264 no. 7
(April, 2018),
pp. 47074748, Elsevier BV [doi] [abs]
 Gao, Y; Liu, JG; Lu, XY; 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, vol. 57 no. 2
(April, 2018), Springer Nature [doi] [abs]
 Feng, Y; Li, L; Liu, JG, Semigroups of stochastic gradient descent and online principal component analysis: Properties and diffusion approximations,
Communications in Mathematical Sciences, vol. 16 no. 3
(January, 2018),
pp. 777789 [doi] [abs]
 Li, L; Liu, JG, Some compactness criteria for weak solutions of time fractional pdes,
Siam Journal on Mathematical Analysis, vol. 50 no. 4
(January, 2018),
pp. 39633995, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]
 Gao, Y; Li, L; Liu, JG, A dispersive regularization for the modified camassa–holm equation,
Siam Journal on Mathematical Analysis, vol. 50 no. 3
(January, 2018),
pp. 28072838, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]
 Li, L; Liu, JG, A generalized definition of caputo derivatives and its application to fractional odes,
Siam Journal on Mathematical Analysis, vol. 50 no. 3
(January, 2018),
pp. 28672900, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]
 Li, L; Liu, JG, A note on deconvolution with completely monotone sequences and discrete fractional calculus,
Quarterly of Applied Mathematics, vol. 76 no. 1
(January, 2018),
pp. 189198, American Mathematical Society (AMS) [doi] [abs]
 Coquel, F; Jin, S; Liu, JG; Wang, L, Entropic subcell shock capturing schemes via JinXin relaxation and glimm front sampling for scalar conservation laws,
Mathematics of Computation, vol. 87 no. 311
(January, 2018),
pp. 10831126, American Mathematical Society (AMS) [doi] [abs]
 Liu, JG; Wang, L; Zhou, Z, Positivitypreserving and asymptotic preserving method for 2D KellerSegal equations,
Mathematics of Computation, vol. 87 no. 311
(January, 2018),
pp. 11651189, American Mathematical Society (AMS) [doi] [abs]
 Gao, Y; Liu, JG, The modified CamassaHolm equation in Lagrangian coordinates,
Discrete & Continuous Dynamical Systems B, vol. 23 no. 6
(2018),
pp. 25452592, American Institute of Mathematical Sciences (AIMS) [doi]
 Li, L; Liu, JG; Lu, J, Fractional Stochastic Differential Equations Satisfying FluctuationDissipation Theorem,
Journal of Statistical Physics, vol. 169 no. 2
(October, 2017),
pp. 316339, Springer Nature America, Inc [doi] [abs]
 Liu, JG; Ma, Z; Zhou, Z, Explicit and Implicit TVD Schemes for Conservation Laws with Caputo Derivatives,
Journal of Scientific Computing, vol. 72 no. 1
(July, 2017),
pp. 291313, Springer Nature [doi] [abs]
 Gao, Y; Ji, H; Liu, JG; Witelski, TP, Global existence of solutions to a tear film model with locally elevated evaporation rates,
Physica D: Nonlinear Phenomena, vol. 350
(July, 2017),
pp. 1325, Elsevier BV [doi] [abs]
 Gao, Y; Liu, JG; Lu, J, Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces,
Journal of Nonlinear Science, vol. 27 no. 3
(June, 2017),
pp. 873926, Springer Nature [doi] [abs]
 Liu, JG; Wang, J, Global existence for a thin film equation with subcritical mass,
Discrete and Continuous Dynamical Systems Series B, vol. 22 no. 4
(June, 2017),
pp. 14611492, American Institute of Mathematical Sciences (AIMS) [doi] [abs]
 Degond, P; Liu, JG; Pego, RL, Coagulation–Fragmentation Model for Animal GroupSize Statistics,
Journal of Nonlinear Science, vol. 27 no. 2
(April, 2017),
pp. 379424, Springer Nature [doi] [abs]
 Cong, W; Liu, JG, Uniform L^{∞} boundedness for a degenerate parabolicparabolic KellerSegel model,
Discrete and Continuous Dynamical Systems Series B, vol. 22 no. 2
(March, 2017),
pp. 307338, American Institute of Mathematical Sciences (AIMS) [doi] [abs]
 Gao, Y; Liu, JG; Lu, J, Weak solution of a continuum model for vicinal surface in the attachmentdetachmentlimited regime,
Siam Journal on Mathematical Analysis, vol. 49 no. 3
(January, 2017),
pp. 17051731, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]
 Liu, JG; Wang, J, A generalized Sz. Nagy inequality in higher dimensions and the critical thin film equation,
Nonlinearity, vol. 30 no. 1
(January, 2017),
pp. 3560, IOP Publishing [doi] [abs]
 Huang, H; Liu, JG, Discreteintime random particle blob method for the KellerSegel equation and convergence analysis,
Communications in Mathematical Sciences, vol. 15 no. 7
(January, 2017),
pp. 18211842, International Press of Boston [doi] [abs]
 Degond, P; Herty, M; Liu, JG, Meanfield games and model predictive control,
Communications in Mathematical Sciences, vol. 15 no. 5
(January, 2017),
pp. 14031422, International Press of Boston [doi] [abs]
 Degond, P; Liu, JG; MerinoAceituno, S; Tardiveau, T, Continuum dynamics of the intention field under weakly cohesive social interaction,
Mathematical Models and Methods in Applied Sciences, vol. 27 no. 1
(January, 2017),
pp. 159182, World Scientific Pub Co Pte Lt [doi] [abs]
 Liu, JG; Yang, R, A random particle blob method for the kellersegel equation and convergence analysis,
Mathematics of Computation, vol. 86 no. 304
(January, 2017),
pp. 725745, American Mathematical Society (AMS) [doi] [abs]
 Gao, Y; Liu, JG, Global convergence of a sticky particle method for the modified CamassaHolm equation,
Siam Journal on Mathematical Analysis, vol. 49 no. 2
(January, 2017),
pp. 12671294, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]
 Liu, JG; Xu, X, Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions,
Siam Journal on Mathematical Analysis, vol. 49 no. 3
(January, 2017),
pp. 22202245, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]
 Huang, H; Liu, JG, Error estimate of a random particle blob method for the KellerSegel equation,
Mathematics of Computation, vol. 86 no. 308
(January, 2017),
pp. 27192744, American Mathematical Society (AMS) [doi] [abs]
 Huang, H; Liu, JG, Error estimates of the aggregationdiffusion splitting algorithms for the KellerSegel equations,
Discrete and Continuous Dynamical Systems Series B, vol. 21 no. 10
(December, 2016),
pp. 34633478, American Institute of Mathematical Sciences (AIMS) [doi] [abs]
 Huang, H; Liu, JG, A note on MongeAmpère KellerSegel equation,
Applied Mathematics Letters, vol. 61
(November, 2016),
pp. 2634, Elsevier BV [doi] [abs]
 Liu, JG; Wang, J, A Note on L∞Bound and Uniqueness to a Degenerate KellerSegel Model,
Acta Applicandae Mathematicae, vol. 142 no. 1
(April, 2016),
pp. 173188, Springer Nature, ISSN 01678019 [doi] [abs]
 Herschlag, G; Liu, JG; Layton, AT, Fluid extraction across pumping and permeable walls in the viscous limit,
Physics of Fluids, vol. 28 no. 4
(April, 2016),
pp. 041902041902, AIP Publishing, ISSN 10706631 [doi] [abs]
 Liu, JG; Wang, J, Refined hypercontractivity and uniqueness for the Keller–Segel equations,
Applied Mathematics Letters, vol. 52
(February, 2016),
pp. 212219, Elsevier BV [doi]
 Chen, J; Liu, JG; Zhou, Z, On a SchrödingerLandauLifshitz system: Variational structure and numerical methods,
Multiscale Modeling & Simulation, vol. 14 no. 4
(January, 2016),
pp. 14631487, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]
 Huang, H; Liu, JG, Wellposedness for the kellersegel equation with fractional laplacian and the theory of propagation of chaos,
Kinetic and Related Models, vol. 9 no. 4
(January, 2016),
pp. 715748 [doi] [abs]
 Cong, W; Liu, JG, A degenerate plaplacian kellersegel model,
Kinetic and Related Models, vol. 9 no. 4
(January, 2016),
pp. 687714, American Institute of Mathematical Sciences (AIMS) [doi] [abs]
 Liu, JG; Xu, X, Existence theorems for a multidimensional crystal surface model,
Siam Journal on Mathematical Analysis, vol. 48 no. 6
(January, 2016),
pp. 36673687, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]
 Liu, JG; Pego, RL, On generating functions of hausdorff moment sequences,
Transactions of the American Mathematical Society, vol. 368 no. 12
(January, 2016),
pp. 84998518, American Mathematical Society (AMS) [doi] [abs]
 Liu, JG; Zhang, Y, Convergence of diffusiondrift many particle systems in probability under a sobolev norm, Proceedings of Particle Systems and Partial Differential Equations  III,
Springer Proceedings in Mathematics and Statistics, vol. 162
(January, 2016),
pp. 195223, Springer International Publishing, ISBN 9783319321424 [doi] [abs]
 J.G. Liu and R. Yang, Propagation of chaos for large Brownian particle system with Coulomb interaction,
Research in the Mathematical Sciences, vol. 3 no. 40
(2016)
 Y. Duan and J.G. Liu, Error estimate of the particle method for the bequation,
Methods and Applications of Analysis, vol. 23
(2016),
pp. 119154
 J.G. Liu and Y. Zhang, Convergence of stochastic interacting particle systems in probability under a Sobolev norm,
Annals of Mathematical Sciences and Applications, vol. 1
(2016),
pp. 251299
 Xue, Y; Wang, C; Liu, JG, Simple Finite Element Numerical Simulation of Incompressible Flow Over Nonrectangular Domains and the SuperConvergence Analysis,
Journal of Scientific Computing, vol. 65 no. 3
(March, 2015),
pp. 11891216, Springer Nature, ISSN 08857474 [doi] [abs]
 Lu, J; Liu, JG; 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, vol. 91 no. 3
(March, 2015),
pp. 032403, ISSN 15393755 [doi] [abs]
 Chertock, A; Liu, JG; Pendleton, T, Elastic collisions among peakon solutions for the CamassaHolm equation,
Applied Numerical Mathematics, vol. 93
(January, 2015),
pp. 3046, Elsevier BV, ISSN 01689274 [doi] [abs]
 Degond, P; Frouvelle, A; Liu, JG, Phase Transitions, Hysteresis, and Hyperbolicity for SelfOrganized Alignment Dynamics,
Archive for Rational Mechanics and Analysis, vol. 216 no. 1
(January, 2015),
pp. 63115 [doi] [abs]
 Herschlag, G; Liu, JG; Layton, AT, An exact solution for stokes flow in a channel with arbitrarily large wall permeability,
Siam Journal on Applied Mathematics, vol. 75 no. 5
(January, 2015),
pp. 22462267, Society for Industrial & Applied Mathematics (SIAM), ISSN 00361399 [doi] [abs]
 Degond, P; Liu, JG; Ringhofer, C, Evolution of wealth in a nonconservative economy driven by local Nash equilibria.,
Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences, vol. 372 no. 2028
(November, 2014),
pp. 2013039420130394, The Royal Society, ISSN 1364503X [doi] [abs]
 Johnston, H; Wang, C; Liu, JG, A Local Pressure Boundary Condition Spectral Collocation Scheme for the ThreeDimensional Navier–Stokes Equations,
Journal of Scientific Computing, vol. 60 no. 3
(September, 2014),
pp. 612626, Springer Nature, ISSN 08857474 [doi] [abs]
 Duan, Y; Liu, JG, Convergence analysis of the vortex blob method for the bequation,
Discrete and Continuous Dynamical Systems Series A, vol. 34 no. 5
(May, 2014),
pp. 19952011, American Institute of Mathematical Sciences (AIMS), ISSN 10780947 [doi] [abs]
 Bian, S; Liu, JG; Zou, C, Ultracontractivity for kellersegel model with diffusion exponent m > 12/d,
Kinetic and Related Models, vol. 7 no. 1
(March, 2014),
pp. 928, American Institute of Mathematical Sciences (AIMS), ISSN 19375093 [doi] [abs]
 Coquel, F; Jin, S; Liu, JG; Wang, L, WellPosedness and Singular Limit of a Semilinear Hyperbolic Relaxation System with a TwoScale Discontinuous Relaxation Rate,
Archive for Rational Mechanics and Analysis, vol. 214 no. 3
(January, 2014),
pp. 10511084, ISSN 00039527 [doi] [abs]
 Degond, P; Herty, M; Liu, JG, Flow on sweeping networks,
Multiscale Modeling & Simulation, vol. 12 no. 2
(January, 2014),
pp. 538565, Society for Industrial & Applied Mathematics (SIAM), ISSN 15403459 [doi] [abs]
 Chen, X; Li, X; Liu, JG, Existence and uniqueness of global weak solution to a kinetic model for the sedimentation of rodlike particles,
Communications in Mathematical Sciences, vol. 12 no. 8
(January, 2014),
pp. 15791601, International Press of Boston, ISSN 15396746 [doi] [abs]
 Degond, P; Frouvelle, A; Liu, JG, A NOTE ON PHASE TRANSITIONS FOR THE SMOLUCHOWSKI EQUATION WITH DIPOLAR POTENTIAL,
in Proceedings of the Fourteenth International Conference on Hyperbolic Problems: Theory, Numerics and Application, edited by Ancona, F; Bressan, A; Marcati, P; Marson, A,
Hyperbolic Problems: Theory, Numerics, Applications, vol. 8
(January, 2014),
pp. 179192, AMER INST MATHEMATICAL SCIENCESAIMS
 Chae, D; Degond, P; Liu, JG, Wellposedness for hallmagnetohydrodynamics,
Annales De L'Institut Henri Poincare (C) Non Linear Analysis, vol. 31 no. 3
(January, 2014),
pp. 555565 [doi] [abs]
 Goudon, T; Jin, S; Liu, JG; Yan, B, Asymptoticpreserving schemes for kineticfluid modeling of disperse twophase flows with variable fluid density,
International Journal for Numerical Methods in Fluids, vol. 75 no. 2
(2014),
pp. 81102, WILEY, ISSN 02712091 [doi] [abs]
 Huang, YL; Liu, JG; Wang, WC, A generalized mac scheme on curvilinear domains,
Siam Journal on Scientific Computing, vol. 35 no. 5
(November, 2013),
pp. B953B986, Society for Industrial & Applied Mathematics (SIAM), ISSN 10648275 [doi] [abs]
 Bian, S; Liu, JG, Dynamic and Steady States for MultiDimensional KellerSegel Model with Diffusion Exponent m > 0,
Communications in Mathematical Physics, vol. 323 no. 3
(November, 2013),
pp. 10171070, Springer Nature, ISSN 00103616 [doi] [abs]
 Chen, X; Liu, JG, Analysis of polymeric flow models and related compactness theorems in weighted spaces,
Siam Journal on Mathematical Analysis, vol. 45 no. 3
(October, 2013),
pp. 11791215, Society for Industrial & Applied Mathematics (SIAM), ISSN 00361410 [doi] [abs]
 Goudon, T; Jin, S; Liu, JG; Yan, B, Asymptoticpreserving schemes for kineticfluid modeling of disperse twophase flows,
Journal of Computational Physics, vol. 246
(August, 2013),
pp. 145164, Elsevier BV, ISSN 00219991 [doi] [abs]
 Degond, P; Frouvelle, A; Liu, JG, Macroscopic limits and phase transition in a system of selfpropelled particles,
Journal of Nonlinear Science, vol. 23 no. 3
(June, 2013),
pp. 427456, Springer Nature, ISSN 09388974 [doi] [abs]
 Chen, X; Liu, JG, Global weak entropy solution to DoiSaintillanShelley model for active and passive rodlike and ellipsoidal particle suspensions,
Journal of Differential Equations, vol. 254 no. 7
(April, 2013),
pp. 27642802, Elsevier BV, ISSN 00220396 [doi] [abs]
 Jin, S; Liu, JG; Wang, L, A domain decomposition method for semilinear hyperbolic systems with twoscale relaxations,
Mathematics of Computation, vol. 82 no. 282
(February, 2013),
pp. 749779, American Mathematical Society (AMS) [doi] [abs]
 P. Degond, A. Frouvelle, J.G. Liu, S Motsch, L Navoret, Macroscopic models of collective motion and selforganization,
Seminaire Laurent Schwartz  EDP et applicatios, vol. 2012  2013
(2013),
pp. 127
 P. Degond, J.G, Liu, S. Motsch, V. Panferov, Hydrodynamic models of selforganized dynamics: derivation and existence theory,
Methods Anal. Appl., vol. 20
(2013),
pp. 89114
 Degond, P; Liu, JG; Ringhofer, C, Evolution of the Distribution of Wealth in an Economic Environment Driven by Local Nash Equilibria,
Journal of Statistical Physics, vol. 154 no. 3
(2013),
pp. 130, Springer Nature, ISSN 00224715 [doi] [abs]
 Chen, X; Jüngel, A; Liu, JG, A Note on AubinLionsDubinskiǐ Lemmas,
Acta Applicandae Mathematicae, vol. 133 no. 1
(2013),
pp. 111, ISSN 01678019 [doi] [abs]
 Degond, P; Liu, JG; Ringhofer, C, LargeScale Dynamics of MeanField Games Driven by Local Nash Equilibria,
Journal of Nonlinear Science, vol. 24 no. 1
(2013),
pp. 123, ISSN 09388974 [doi] [abs]
 Chae, D; Degond, P; Liu, JG, Wellposedness for Hallmagnetohydrodynamics,
Annales De L'Institut Henri Poincare (C) Non Linear Analysis, vol. 31 no. 3
(2013),
pp. 555565, Elsevier BV, ISSN 02941449 [doi] [abs]
 Haack, J; Jin, S; Liu, JG, An allspeed asymptoticpreserving method for the isentropic Euler and NavierStokes equations,
Communications in Computational Physics, vol. 12 no. 4
(October, 2012),
pp. 955980, Global Science Press, ISSN 18152406 [doi] [abs]
 Chae, D; Liu, JG, Blowup, Zero α Limit and the Liouville Type Theorem for the EulerPoincaré Equations,
Communications in Mathematical Physics, vol. 314 no. 3
(September, 2012),
pp. 671687, Springer Nature, ISSN 00103616 [doi] [abs]
 Carrillo, JA; Chen, L; Liu, JG; Wang, J, A note on the subcritical two dimensional KellerSegel system,
Acta Applicandae Mathematicae, vol. 119 no. 1
(June, 2012),
pp. 4355, Springer Nature, ISSN 01678019 [doi] [abs]
 Chen, L; Liu, JG; Wang, J, Multidimensional degenerate KellerSegel system with critical diffusion exponent 2n/(n + 2),
Siam Journal on Mathematical Analysis, vol. 44 no. 2
(May, 2012),
pp. 10771102, Society for Industrial & Applied Mathematics (SIAM), ISSN 00361410 [doi] [abs]
 Frouvelle, A; Liu, JG, Dynamics in a kinetic model of oriented particles with phase transition,
Siam Journal on Mathematical Analysis, vol. 44 no. 2
(May, 2012),
pp. 791826, Society for Industrial & Applied Mathematics (SIAM), ISSN 00361410 [doi] [abs]
 Chertock, A; Liu, JG; Pendleton, T, Convergence of a particle method and global weak solutions of a family of evolutionary PDEs,
Siam Journal on Numerical Analysis, vol. 50 no. 1
(May, 2012),
pp. 121, Society for Industrial & Applied Mathematics (SIAM), ISSN 00361429 [doi] [abs]
 Degond, P; Liu, JG, Hydrodynamics of selfalignment interactions with precession and derivation of the LandauLifschitzGilbert equation,
Mathematical Models and Methods in Applied Sciences, vol. 22 no. SUPPL.1
(April, 2012),
pp. 11400011140001, World Scientific Pub Co Pte Lt, ISSN 02182025 [doi] [abs]
 Chen, X; Liu, JG, Two nonlinear compactness theorems in L^{p}(0,T;B),
Applied Mathematics Letters, vol. 25 no. 12
(January, 2012),
pp. 22522257, Elsevier BV, ISSN 08939659 [doi] [abs]
 A. Chertock, J.G. Liu, and T. Pendleton, Convergence analysis of the particle method for the CamassaHolm equation,
in Proceedings of the 13th International Conference on ``Hyperbolic Problems: Theory, Numerics and Applications"
(2012),
pp. 365373, Higher Education Press, Beijing
 Acheritogaray, M; Degond, P; Frouvelle, A; Liu, JG, Kinetic formulation and global existence for the hallmagnetohydrodynamics system,
Kinetic and Related Models, vol. 4 no. 4
(December, 2011),
pp. 901918, American Institute of Mathematical Sciences (AIMS), ISSN 19375093 [doi] [abs]
 Zheng, W; Gao, H; Liu, JG; Zhang, Y; Ye, Q; Swank, C, General solution to gradientinduced transverse and longitudinal relaxation of spins undergoing restricted diffusion,
Physical Review A, vol. 84 no. 5
(November, 2011),
pp. 0534118, American Physical Society (APS), ISSN 10502947 [doi] [abs]
 Liu, JG; Lorz, A, A coupled chemotaxisfluid model: Global existence,
Annales De L'Institut Henri Poincare (C) Non Linear Analysis, vol. 28 no. 5
(January, 2011),
pp. 643652, Elsevier BV, ISSN 02941449 [doi] [abs]
 Huang, YL; Liu, JG; Wang, WC, An FFT based fast poisson solver on spherical shells,
Communications in Computational Physics, vol. 9 no. 3
(January, 2011),
pp. 649667, Global Science Press, ISSN 18152406 [doi] [abs]
 Liu, JG; Pego, RL, STABLE DISCRETIZATION OF MAGNETOHYDRODYNAMICS IN BOUNDED DOMAINS,
Communications in Mathematical Sciences, vol. 8 no. 1
(March, 2010),
pp. 234251, INT PRESS BOSTON, INC, ISSN 15396746 [abs]
 Liu, JG; Liu, J; Pego, RL, Stable and accurate pressure approximation for unsteady incompressible viscous flow,
Journal of Computational Physics, vol. 229 no. 9
(January, 2010),
pp. 34283453, Elsevier BV, ISSN 00219991 [doi] [abs]
 Liu, JG; Mieussens, L, Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit,
Siam Journal on Numerical Analysis, vol. 48 no. 4
(January, 2010),
pp. 14741491, Society for Industrial & Applied Mathematics (SIAM), ISSN 00361429 [repository], [doi] [abs]
 Liu, JG; Pego, RL, Stable discretization of magnetohydrodynamics in bounded domains,
Communications in Mathematical Sciences, vol. 8 no. 1
(January, 2010),
pp. 235251, International Press of Boston, ISSN 15396746 [doi] [abs]
 Liu, JG; Liu, J; Pego, RL, Error estimates for finiteelement NavierStokes solvers without standard InfSup conditions,
Chinese Annals of Mathematics, Series B, vol. 30 no. 6
(December, 2009),
pp. 743768, Springer Nature, ISSN 02529599 [doi] [abs]
 Liu, JG; Wang, WC, Characterization and regularity for axisymmetric solenoidal vector fields with application to navierstokes equation,
Siam Journal on Mathematical Analysis, vol. 41 no. 5
(December, 2009),
pp. 18251850, Society for Industrial & Applied Mathematics (SIAM), ISSN 00361410 [doi] [abs]
 Ha, SY; Liu, JG, A simple proof of the CuckerSmale flocking dynamics and meanfield limit,
Communications in Mathematical Sciences, vol. 7 no. 2
(January, 2009),
pp. 297325, International Press of Boston, ISSN 15396746 [doi] [abs]
 Degond, P; Liu, JG; Vignal, MH, Analysis of an asymptotic preserving scheme for the EulerPoisson system in the quasineutral limit,
Siam Journal on Numerical Analysis, vol. 46 no. 3
(November, 2008),
pp. 12981322, Society for Industrial & Applied Mathematics (SIAM), ISSN 00361429 [doi] [abs]
 Lin, P; Liu, JG; Lu, X, Long time numerical solution of the NavierStokes equations based on a sequential regularization formulation,
Siam Journal on Scientific Computing, vol. 31 no. 1
(November, 2008),
pp. 398419, Society for Industrial & Applied Mathematics (SIAM), ISSN 10648275 [doi] [abs]
 Lu, X; Lin, P; Liu, JG, Analysis of a sequential regularization method for the unsteady NavierStokes equations,
Mathematics of Computation, vol. 77 no. 263
(July, 2008),
pp. 14671494, American Mathematical Society (AMS), ISSN 00255718 [doi] [abs]
 Liu, JG; Wang, C, A fourth order numerical method for the primtive equations formulated in mean vorticity,
Communications in Computational Physics, vol. 4 no. 1
(January, 2008),
pp. 2655, ISSN 18152406 [abs]
 Hsia, CH; Liu, JG; Wang, C, Structural stability and bifurcation for 2D incompressible ows with symmetry,
Meth. Appl. Anal., vol. 15
(2008),
pp. 495512
 Antman, SS; Liu, JG, Basic themes and pretty problems of nonlinear solid mechanics,
Milan Journal of Mathematics, vol. 75 no. 1
(December, 2007),
pp. 135176, Springer Nature, ISSN 14249286 [doi] [abs]
 Moore, J; Cheng, Z; Hao, J; Guo, G; Liu, JG; Lin, C; Yu, LL, 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, vol. 55 no. 25
(December, 2007),
pp. 1017310182, ISSN 00218561 (published on Web 10/30/2007.) [doi] [abs]
 Liu, JG; Liu, J; Pego, RL, Stability and convergence of efficient NavierStokes solvers via a commutator estimate,
Communications on Pure and Applied Mathematics, vol. 60 no. 10
(October, 2007),
pp. 14431487, WILEY, ISSN 00103640 [doi] [abs]
 J.G. Liu, Jie Liu and R. Pego, Estimates on the Stokes pressure by partitioning the energy of harmonic functions,
in Kyoto Conference on the NavierStokes equations and their Applications, edited by Y. Giga, H. Kozono, H. Okamoto and Y. Shibta
(2007),
pp. 251270, Kyoto Univ. [abs]
 Liu, JG; Liu, J; Pego, R, Stability and convergence of efficient NavierStokes solvers via a commutator estimate via a commutator estimate,
Comm. Pure Appl. Math., vol. 60
(2007),
pp. 14431487
 Degond, P; Jin, S; Liu, JG, Machnumber uniform asymptotic preserving Gauge schemes for compressible flows,
Bulletin of the Institute of Mathematics Academia Sinica (New Series), vol. 2
(2007),
pp. 851892 [abs]
 Liu, JG; Wang, WC, Convergence analysis of the energy and helicity preserving scheme for axisymmetric flows,
Siam Journal on Numerical Analysis, vol. 44 no. 6
(December, 2006),
pp. 24562480, Society for Industrial & Applied Mathematics (SIAM), ISSN 00361429 [doi] [abs]
 Degond, P; Liu, JG; Mieussens, L, Macroscopic fluid models with localized kinetic upscaling effects,
Multiscale Modeling & Simulation, vol. 5 no. 3
(September, 2006),
pp. 940979, Society for Industrial & Applied Mathematics (SIAM), ISSN 15403459 [doi] [abs]
 Moore, J; Liu, JG; Zhou, K; Yu, LL, Effects of genotype and environment on the antioxidant properties of hard winter wheat bran.,
Journal of Agricultural and Food Chemistry, vol. 54 no. 15
(July, 2006),
pp. 53135322, ISSN 00218561 [doi] [abs]
 Liu, JG; Samelson, R; Wang, C, Global weak solution of planetary geostrophic equations with inviscid geostrophic balance,
International Journal of Phytoremediation, vol. 85 no. 67
(January, 2006),
pp. 593605 [doi] [abs]
 J.G. Liu, Jie Liu and R. Pego, On incompressible NavierStokes dynamics: a new approach for analysis and computation,
in Proceedings of the Tenth International Conference on Hyperbolic Problems, edited by F. Asakura, etc
(2006),
pp. 2944, Yokohama Publishers, Inc.
 Liu, JG; Wang, WC, Energy and helicity preserving schemes for hydro and magnetohydrodynamics flows with symmetry,
Journal of Computational Physics, vol. 200 no. 1
(October, 2004),
pp. 833, Elsevier BV [doi] [abs]
 Ghil, M; Liu, JG; Wang, C; Wang, S, Boundarylayer separation and adverse pressure gradient for 2D viscous incompressible flow,
Physica D: Nonlinear Phenomena, vol. 197 no. 12
(October, 2004),
pp. 149173, Elsevier BV, ISSN 01672789 [doi] [abs]
 Li, B; Liu, JG, Epitaxial growth without slope selection: Energetics, coarsening, and dynamic scaling,
Journal of Nonlinear Science, vol. 14 no. 5
(October, 2004),
pp. 429451, Springer Nature, ISSN 09388974 [doi] [abs]
 Johnston, H; Liu, JG, Accurate, stable and efficient NavierStokes solvers based on explicit treatment of the pressure term,
Journal of Computational Physics, vol. 199 no. 1
(September, 2004),
pp. 221259, Elsevier BV [doi] [abs]
 Lin, HE; Liu, JG; Xu, WQ, Effects of small viscosity and far field boundary conditions for hyperbolic systems,
Communications on Pure and Applied Analysis, vol. 3 no. 2
(June, 2004),
pp. 267290, American Institute of Mathematical Sciences (AIMS), ISSN 15340392 [doi] [abs]
 Wang, C; Liu, JG; Johnston, H, Analysis of a fourth order finite difference method for the incompressible Boussinesq equations,
Numerische Mathematik, vol. 97 no. 3
(May, 2004),
pp. 555594, Springer Nature [doi] [abs]
 Liu, JG; Xu, WQ, Far field boundary condition for convection diffusion equation at zero viscosity limit,
Quarterly of Applied Mathematics, vol. 62 no. 1
(January, 2004),
pp. 2752, American Mathematical Society (AMS) [doi] [abs]
 Liu, JG; Wang, C, High order finite difference methods for unsteady incompressible flows in multiconnected domains,
Computers & Fluids, vol. 33 no. 2
(January, 2004),
pp. 223255, Elsevier BV [doi] [abs]
 Li, B; Liu, JG, Eptaxial growth without slope selection: energetics, coarsening, and dynamic scaling,
J. Nonlinear Sci., vol. 14 no. 5
(2004),
pp. 429451, ISSN 09388974 [doi] [abs]
 Liu, JG; Wang, C, High order finite difference method for unsteady incompressible flow on multiconnected domain in vorticitystream function formulation,
Computer and Fluids, vol. 33 no. 2
(2004),
pp. 223255 [doi] [abs]
 Li, B; Liu, JG, Thin film epitaxy with or without slope selection,
European Journal of Applied Mathematics, vol. 14 no. 6
(December, 2003),
pp. 713743, Cambridge University Press (CUP) [doi] [abs]
 Wang, C; Liu, JG, Positivity property of secondorder fluxsplitting schemes for the compressible Euler equations,
Discrete and Continuous Dynamical Systems Series B, vol. 3 no. 2
(May, 2003),
pp. 201228, American Institute of Mathematical Sciences (AIMS) [doi] [abs]
 Liu, JG; Wang, C; Johnston, H, A Fourth Order Scheme for Incompressible Boussinesq Equations,
Journal of Scientific Computing, vol. 18 no. 2
(April, 2003),
pp. 253285, ISSN 08857474 [doi] [abs]
 ChainaisHillairet, C; Liu, JG; Peng, YJ, Finite volume scheme for multidimensional driftdiffusion equations and convergence analysis,
Esaim: Mathematical Modelling and Numerical Analysis, vol. 37 no. 2
(January, 2003),
pp. 319338, E D P SCIENCES [doi] [abs]
 Wang, C; Liu, JG, Fourth order convergence of a compact difference solver for incompressible flow,
Commun. Appl. Anal., vol. 7
(2003),
pp. 171191
 Duraisamy, K; Baeder, JD; Liu, JG, Concepts and Application of TimeLimiters to High Resolution Schemes,
Journal of Scientific Computing, vol. 19 no. 13
(2003),
pp. 139162, ISSN 08857474 [doi] [abs]
 Weinan, E; Liu, JG, Gauge method for viscous incompressible flows,
Comm. Math. Sci., vol. 1
(2003),
pp. 317332
 Chern, IL; Liu, JG; Wang, WC, Accurate evaluation of electrostatics for macromolecules in solution,
Methods and Applications of Analysis, vol. 10
(2003),
pp. 309328
 Johnston, H; Liu, JG, Finite difference schemes for incompressible flow based on local pressure boundary conditions,
Journal of Computational Physics, vol. 180 no. 1
(July, 2002),
pp. 120154, Elsevier BV, ISSN 00219991 [doi] [abs]
 Wang, C; Liu, JG, Analysis of finite difference schemes for unsteady NavierStokes equations in vorticity formulation,
Numerische Mathematik, vol. 91 no. 3
(May, 2002),
pp. 543576 [doi] [abs]
 Weinan, E; Liu, JG, Projection method III: Spatial discretization on the staggered grid,
Mathematics of Computation, vol. 71 no. 237
(January, 2002),
pp. 2747, American Mathematical Society (AMS) [doi] [abs]
 Liu, JG; Wang, WC, An energypreserving MACYee scheme for the incompressible MHD equation,
Journal of Computational Physics, vol. 174 no. 1
(November, 2001),
pp. 1237, Elsevier BV, ISSN 00219991 [doi] [abs]
 Liu, JG; Xin, Z, Convergence of the point vortex method for 2D vortex sheet,
Mathematics of Computation, vol. 70 no. 234
(April, 2001),
pp. 595606, American Mathematical Society (AMS) [doi] [abs]
 Liu, JG; Weinan, E, Simple finite element method in vorticity formulation for incompressible flows,
Mathematics of Computation, vol. 70 no. 234
(April, 2001),
pp. 579593, American Mathematical Society (AMS) [doi] [abs]
 Liu, JG; Weinan, E, Simple finite element method in vorticity formulation for incompressible flow,
Math. Comp., vol. 69
(2001),
pp. 13851407
 Liu, JG; Xin, Z, Convergence of point vortex method for 2D vortex sheet,
Math. Comp., vol. 70 no. 234
(2001),
pp. 565606 [doi] [abs]
 Weinan, E; Liu, JG, Gauge finite element method for incompressible flows,
International Journal for Numerical Methods in Fluids, vol. 34 no. 8
(December, 2000),
pp. 701710, WILEY, ISSN 02712091 [doi] [abs]
 Wang, C; Liu, JG, Convergence of gauge method for incompressible flow,
Mathematics of Computation, vol. 69 no. 232
(October, 2000),
pp. 13851407 [abs]
 Liu, JG; Shu, CW, A HighOrder Discontinuous Galerkin Method for 2D Incompressible Flows,
Journal of Computational Physics, vol. 160 no. 2
(May, 2000),
pp. 577596, Elsevier BV [doi] [abs]
 Liu, JG; Xin, Z, Convergence of a Galerkin method for 2D discontinuous Euler flows,
Communications on Pure and Applied Mathematics, vol. 53 no. 6
(January, 2000),
pp. 786798, WILEY [doi] [abs]
 Lefloch, PG; Liu, JG, Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions,
Mathematics of Computation, vol. 68 no. 227
(July, 1999),
pp. 10251055 [abs]
 Wang, ZJ; Liu, JG; Childress, S, Connection between corner vortices and shear layer instability in flow past an ellipse,
Physics of Fluids, vol. 11 no. 9
(January, 1999),
pp. 24462448 [doi] [abs]
 Choi, H; Liu, JG, The Reconstruction of Upwind Fluxes for Conservation Laws: Its Behavior in Dynamic and Steady State Calculations,
Journal of Computational Physics, vol. 144 no. 2
(August, 1998),
pp. 237256, Elsevier BV [doi] [abs]
 Xu, E; Liu, JG, Pricing of mortgagebacked securities with optionadjusted spread,
Managerial Finance, vol. 24
(1998),
pp. 94109
 E, W; Liu, JG, Finite Difference Methods for 3D Viscous Incompressible Flows in the VorticityVector Potential Formulation on Nonstaggered Grids,
Journal of Computational Physics, vol. 138 no. 1
(November, 1997),
pp. 5782, Elsevier BV [doi] [abs]
 Chen, GQ; Liu, JG, Convergence of difference schemes with high resolution for conservation laws,
Mathematics of Computation, vol. 66 no. 219
(July, 1997),
pp. 10271053 [abs]
 Weinan, E; Liu, JG, Finite difference schemes for incompressible flows in the velocity  impulse density formulation,
Journal of Computational Physics, vol. 130 no. 1
(January, 1997),
pp. 6776, Elsevier BV [doi] [abs]
 Liu, JG; Xin, Z, Boundarylayer behavior in the fluiddynamic limit for a nonlinear model Boltzmann equation,
Archive for Rational Mechanics and Analysis, vol. 135 no. 1
(October, 1996),
pp. 61105, Springer Nature [doi] [abs]
 Weinan, E; Liu, JG, Projection method II: GodunovRyabenki analysis,
Siam Journal on Numerical Analysis, vol. 33 no. 4
(August, 1996),
pp. 15971621, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]
 Weinan, E; Liu, JG, Vorticity boundary condition and related issues for finite difference schemes,
Journal of Computational Physics, vol. 124 no. 2
(March, 1996),
pp. 368382, Elsevier BV [doi] [abs]
 Jin, S; Liu, JG, The effects of numerical viscosities: I. Slowly moving shocks,
Journal of Computational Physics, vol. 126 no. 2
(January, 1996),
pp. 373389, Elsevier BV [doi] [abs]
 Weinan, E; Liu, JG, Essentially compact schemes for unsteady viscous incompressible flows,
Journal of Computational Physics, vol. 126 no. 1
(January, 1996),
pp. 122138, Elsevier BV [doi] [abs]
 Levermore, CD; Liu, JG, Large oscillations arising in a dispersive numerical scheme,
Physica D: Nonlinear Phenomena, vol. 99 no. 23
(January, 1996),
pp. 191216, Elsevier BV [doi] [abs]
 Liu, JG; Xin, Z, Kinetic and viscous boundary layers for broadwell equations,
Transport Theory and Statistical Physics, vol. 25 no. 35
(January, 1996),
pp. 447461, Informa UK Limited [doi] [abs]
 Jin, S; Liu, JG, Oscillations induced by numerical viscosities,
Mat. Contemp., vol. 10
(1996),
pp. 169180
 Liu, J; Xin, Z, Convergence of vortex methods for weak solutions to the 2‐D euler equations with vortex sheet data,
Communications on Pure and Applied Mathematics, vol. 48 no. 6
(January, 1995),
pp. 611628 [doi] [abs]
 Weinan, E; Liu, JG, Projection method I: convergence and numerical boundary layers,
Siam J. Numer. Anal., vol. 32
(1995),
pp. 10171057
 Jin, S; Liu, JG, Relaxation and diffusion enhanced dispersive waves,
Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, vol. 446 no. 1928
(September, 1994),
pp. 555563 [abs]
 Lefloch, P; Liu, JG, Discrete entropy and monotonicity criteria for hyperbolic conservation laws,
C.R. Acad. Sci. Paris., vol. 319
(1994),
pp. 881886
 Liu, JG; Xin, Z, Nonlinear stability of discrete shocks for systems of conservation laws,
Archive for Rational Mechanics and Analysis, vol. 125 no. 3
(September, 1993),
pp. 217256, Springer Nature, ISSN 00039527 [doi] [abs]
 Chen, GQ; Liu, JG, Convergence of secondorder schemes for isentropic gas dynamics,
Mathematics of Computation, vol. 61 no. 204
(January, 1993),
pp. 607627, American Mathematical Society (AMS) [doi] [abs]
 Engquist, B; Liu, J, Numerical methods for oscillatory solutions to hyperbolic problems,
Communications on Pure and Applied Mathematics, vol. 46 no. 10
(January, 1993),
pp. 13271361, WILEY [doi] [abs]
 Liu, JG; Xin, Z, L^{1}stability of stationary discrete shocks,
Mathematics of Computation, vol. 60 no. 201
(January, 1993),
pp. 233244, American Mathematical Society (AMS) [doi] [abs]
Papers Accepted
 P. Degond, J.G. Liu, S. MerinoAceituno, T. Tardiveau, Continuum dynamics of the intention field under weakly cohesive social interactions,
Math. Models Methods Appl. Sci.
(2016)
 Y. Gao, J.G. Liu, J. Lu, Continuum limit of a mesoscopic model of step motion on vicinal surfaces,
J. Nonlinear Science
(2016)


dept@math.duke.edu
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Mathematics Department
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