Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke





.......................

.......................


Publications of Jian-Guo Liu    :chronological  alphabetical  combined  bibtex listing:

Books

  1. Multi-scale phenomena in complex fluids, Modeling, Analysis and Numerical Simulations, edited by T. Hou, C. Liu and J.-G. Liu (2009), World Scientific, ISBN 978-981-4273-25-1
  2. 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 978-0-8218-4728-2
  3. Dynamics in Models of Coarsening, Coagulation, Condensation and Quantization, edited by W. Bao and J.-G. Liu (2007), World Scientific, ISBN 9789812708502

Papers Published

  1. 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. 54-67 [doi]  [abs]
  2. Lafata, KJ; Hong, JC; Geng, R; Ackerson, BG; Liu, J-G; Zhou, Z; Torok, J; Kelsey, CR; Yin, F-F, Association of pre-treatment radiomic features with lung cancer recurrence following stereotactic body radiation therapy., Phys Med Biol, vol. 64 no. 2 (January, 2019), pp. 025007 [doi]  [abs]
  3. 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. 1-29 [doi]  [abs]
  4. 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. 4433-4453, American Institute of Mathematical Sciences (AIMS) [doi]  [abs]
  5. 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. 3109-3135, American Institute of Mathematical Sciences (AIMS) [doi]  [abs]
  6. Feng, Y; Li, L; Liu, JG; Xu, X, A note on one-dimensional time fractional ODEs, Applied Mathematics Letters, vol. 83 (September, 2018), pp. 87-94, Elsevier BV [doi]  [abs]
  7. 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. 1044-1096, Elsevier BV [doi]  [abs]
  8. 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. 73-94, Elsevier BV [doi]  [abs]
  9. Chen, K; Li, Q; Liu, JG, Online learning in optical tomography: A stochastic approach, Inverse Problems, vol. 34 no. 7 (May, 2018), pp. 075010-075010, IOP Publishing [doi]  [abs]
  10. 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. 5489-5526, ACADEMIC PRESS INC ELSEVIER SCIENCE [doi]  [abs]
  11. Li, L; Liu, JG, p-Euler equations and p-Navier–Stokes equations, Journal of Differential Equations, vol. 264 no. 7 (April, 2018), pp. 4707-4748, Elsevier BV [doi]  [abs]
  12. 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]
  13. 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. 777-789 [doi]  [abs]
  14. 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. 3963-3995, Society for Industrial & Applied Mathematics (SIAM) [doi]  [abs]
  15. 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. 2807-2838, Society for Industrial & Applied Mathematics (SIAM) [doi]  [abs]
  16. 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. 2867-2900, Society for Industrial & Applied Mathematics (SIAM) [doi]  [abs]
  17. 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. 189-198, American Mathematical Society (AMS) [doi]  [abs]
  18. Coquel, F; Jin, S; Liu, JG; Wang, L, Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and glimm front sampling for scalar conservation laws, Mathematics of Computation, vol. 87 no. 311 (January, 2018), pp. 1083-1126, American Mathematical Society (AMS) [doi]  [abs]
  19. Liu, JG; Wang, L; Zhou, Z, Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations, Mathematics of Computation, vol. 87 no. 311 (January, 2018), pp. 1165-1189, American Mathematical Society (AMS) [doi]  [abs]
  20. Gao, Y; Liu, J-G, The modified Camassa-Holm equation in Lagrangian coordinates, Discrete & Continuous Dynamical Systems B, vol. 23 no. 6 (2018), pp. 2545-2592, American Institute of Mathematical Sciences (AIMS) [doi]
  21. Li, L; Liu, JG; Lu, J, Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem, Journal of Statistical Physics, vol. 169 no. 2 (October, 2017), pp. 316-339, Springer Nature America, Inc [doi]  [abs]
  22. 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. 291-313, Springer Nature [doi]  [abs]
  23. 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. 13-25, Elsevier BV [doi]  [abs]
  24. 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. 873-926, Springer Nature [doi]  [abs]
  25. 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. 1461-1492, American Institute of Mathematical Sciences (AIMS) [doi]  [abs]
  26. Degond, P; Liu, JG; Pego, RL, Coagulation–Fragmentation Model for Animal Group-Size Statistics, Journal of Nonlinear Science, vol. 27 no. 2 (April, 2017), pp. 379-424, Springer Nature [doi]  [abs]
  27. Cong, W; Liu, JG, Uniform L boundedness for a degenerate parabolic-parabolic Keller-Segel model, Discrete and Continuous Dynamical Systems Series B, vol. 22 no. 2 (March, 2017), pp. 307-338, American Institute of Mathematical Sciences (AIMS) [doi]  [abs]
  28. Gao, Y; Liu, JG; Lu, J, Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime, Siam Journal on Mathematical Analysis, vol. 49 no. 3 (January, 2017), pp. 1705-1731, Society for Industrial & Applied Mathematics (SIAM) [doi]  [abs]
  29. 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. 35-60, IOP Publishing [doi]  [abs]
  30. Huang, H; Liu, JG, Discrete-in-time random particle blob method for the Keller-Segel equation and convergence analysis, Communications in Mathematical Sciences, vol. 15 no. 7 (January, 2017), pp. 1821-1842, International Press of Boston [doi]  [abs]
  31. Degond, P; Herty, M; Liu, JG, Meanfield games and model predictive control, Communications in Mathematical Sciences, vol. 15 no. 5 (January, 2017), pp. 1403-1422, International Press of Boston [doi]  [abs]
  32. Degond, P; Liu, JG; Merino-Aceituno, 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. 159-182, World Scientific Pub Co Pte Lt [doi]  [abs]
  33. Liu, JG; Yang, R, A random particle blob method for the keller-segel equation and convergence analysis, Mathematics of Computation, vol. 86 no. 304 (January, 2017), pp. 725-745, American Mathematical Society (AMS) [doi]  [abs]
  34. Gao, Y; Liu, JG, Global convergence of a sticky particle method for the modified Camassa-Holm equation, Siam Journal on Mathematical Analysis, vol. 49 no. 2 (January, 2017), pp. 1267-1294, Society for Industrial & Applied Mathematics (SIAM) [doi]  [abs]
  35. 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. 2220-2245, Society for Industrial & Applied Mathematics (SIAM) [doi]  [abs]
  36. Huang, H; Liu, JG, Error estimate of a random particle blob method for the Keller-Segel equation, Mathematics of Computation, vol. 86 no. 308 (January, 2017), pp. 2719-2744, American Mathematical Society (AMS) [doi]  [abs]
  37. Huang, H; Liu, JG, Error estimates of the aggregation-diffusion splitting algorithms for the Keller-Segel equations, Discrete and Continuous Dynamical Systems Series B, vol. 21 no. 10 (December, 2016), pp. 3463-3478, American Institute of Mathematical Sciences (AIMS) [doi]  [abs]
  38. Huang, H; Liu, JG, A note on Monge-Ampère Keller-Segel equation, Applied Mathematics Letters, vol. 61 (November, 2016), pp. 26-34, Elsevier BV [doi]  [abs]
  39. Liu, JG; Wang, J, A Note on L∞-Bound and Uniqueness to a Degenerate Keller-Segel Model, Acta Applicandae Mathematicae, vol. 142 no. 1 (April, 2016), pp. 173-188, Springer Nature, ISSN 0167-8019 [doi]  [abs]
  40. 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. 041902-041902, AIP Publishing, ISSN 1070-6631 [doi]  [abs]
  41. Liu, J-G; Wang, J, Refined hyper-contractivity and uniqueness for the Keller–Segel equations, Applied Mathematics Letters, vol. 52 (February, 2016), pp. 212-219, Elsevier BV [doi]
  42. Chen, J; Liu, JG; Zhou, Z, On a Schrödinger-Landau-Lifshitz system: Variational structure and numerical methods, Multiscale Modeling & Simulation, vol. 14 no. 4 (January, 2016), pp. 1463-1487, Society for Industrial & Applied Mathematics (SIAM) [doi]  [abs]
  43. Huang, H; Liu, JG, Well-posedness for the keller-segel equation with fractional laplacian and the theory of propagation of chaos, Kinetic and Related Models, vol. 9 no. 4 (January, 2016), pp. 715-748 [doi]  [abs]
  44. Cong, W; Liu, JG, A degenerate p-laplacian keller-segel model, Kinetic and Related Models, vol. 9 no. 4 (January, 2016), pp. 687-714, American Institute of Mathematical Sciences (AIMS) [doi]  [abs]
  45. Liu, JG; Xu, X, Existence theorems for a multidimensional crystal surface model, Siam Journal on Mathematical Analysis, vol. 48 no. 6 (January, 2016), pp. 3667-3687, Society for Industrial & Applied Mathematics (SIAM) [doi]  [abs]
  46. Liu, JG; Pego, RL, On generating functions of hausdorff moment sequences, Transactions of the American Mathematical Society, vol. 368 no. 12 (January, 2016), pp. 8499-8518, American Mathematical Society (AMS) [doi]  [abs]
  47. Liu, JG; Zhang, Y, Convergence of diffusion-drift 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. 195-223, Springer International Publishing, ISBN 9783319321424 [doi]  [abs]
  48. 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)
  49. Y. Duan and J.-G. Liu, Error estimate of the particle method for the b-equation, Methods and Applications of Analysis, vol. 23 (2016), pp. 119-154
  50. 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. 251-299
  51. Xue, Y; Wang, C; Liu, JG, Simple Finite Element Numerical Simulation of Incompressible Flow Over Non-rectangular Domains and the Super-Convergence Analysis, Journal of Scientific Computing, vol. 65 no. 3 (March, 2015), pp. 1189-1216, Springer Nature, ISSN 0885-7474 [doi]  [abs]
  52. 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 1539-3755 [doi]  [abs]
  53. Chertock, A; Liu, JG; Pendleton, T, Elastic collisions among peakon solutions for the Camassa-Holm equation, Applied Numerical Mathematics, vol. 93 (January, 2015), pp. 30-46, Elsevier BV, ISSN 0168-9274 [doi]  [abs]
  54. Degond, P; Frouvelle, A; Liu, JG, Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics, Archive for Rational Mechanics and Analysis, vol. 216 no. 1 (January, 2015), pp. 63-115 [doi]  [abs]
  55. 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. 2246-2267, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1399 [doi]  [abs]
  56. Degond, P; Liu, J-G; Ringhofer, C, Evolution of wealth in a non-conservative economy driven by local Nash equilibria., Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences, vol. 372 no. 2028 (November, 2014), pp. 20130394-20130394, The Royal Society, ISSN 1364-503X [doi]  [abs]
  57. Johnston, H; Wang, C; Liu, JG, A Local Pressure Boundary Condition Spectral Collocation Scheme for the Three-Dimensional Navier–Stokes Equations, Journal of Scientific Computing, vol. 60 no. 3 (September, 2014), pp. 612-626, Springer Nature, ISSN 0885-7474 [doi]  [abs]
  58. Duan, Y; Liu, JG, Convergence analysis of the vortex blob method for the b-equation, Discrete and Continuous Dynamical Systems Series A, vol. 34 no. 5 (May, 2014), pp. 1995-2011, American Institute of Mathematical Sciences (AIMS), ISSN 1078-0947 [doi]  [abs]
  59. Bian, S; Liu, JG; Zou, C, Ultra-contractivity for keller-segel model with diffusion exponent m > 1-2/d, Kinetic and Related Models, vol. 7 no. 1 (March, 2014), pp. 9-28, American Institute of Mathematical Sciences (AIMS), ISSN 1937-5093 [doi]  [abs]
  60. Coquel, F; Jin, S; Liu, JG; 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, vol. 214 no. 3 (January, 2014), pp. 1051-1084, ISSN 0003-9527 [doi]  [abs]
  61. Degond, P; Herty, M; Liu, JG, Flow on sweeping networks, Multiscale Modeling & Simulation, vol. 12 no. 2 (January, 2014), pp. 538-565, Society for Industrial & Applied Mathematics (SIAM), ISSN 1540-3459 [doi]  [abs]
  62. Chen, X; Li, X; Liu, JG, Existence and uniqueness of global weak solution to a kinetic model for the sedimentation of rod-like particles, Communications in Mathematical Sciences, vol. 12 no. 8 (January, 2014), pp. 1579-1601, International Press of Boston, ISSN 1539-6746 [doi]  [abs]
  63. Degond, P; Frouvelle, A; Liu, J-G, 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. 179-192, AMER INST MATHEMATICAL SCIENCES-AIMS
  64. Chae, D; Degond, P; Liu, JG, Well-posedness for hall-magnetohydrodynamics, Annales De L'Institut Henri Poincare (C) Non Linear Analysis, vol. 31 no. 3 (January, 2014), pp. 555-565 [doi]  [abs]
  65. Goudon, T; Jin, S; Liu, J-G; 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, vol. 75 no. 2 (2014), pp. 81-102, WILEY, ISSN 0271-2091 [doi]  [abs]
  66. 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. B953-B986, Society for Industrial & Applied Mathematics (SIAM), ISSN 1064-8275 [doi]  [abs]
  67. Bian, S; Liu, JG, Dynamic and Steady States for Multi-Dimensional Keller-Segel Model with Diffusion Exponent m > 0, Communications in Mathematical Physics, vol. 323 no. 3 (November, 2013), pp. 1017-1070, Springer Nature, ISSN 0010-3616 [doi]  [abs]
  68. 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. 1179-1215, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410 [doi]  [abs]
  69. Goudon, T; Jin, S; Liu, JG; Yan, B, Asymptotic-preserving schemes for kinetic-fluid modeling of disperse two-phase flows, Journal of Computational Physics, vol. 246 (August, 2013), pp. 145-164, Elsevier BV, ISSN 0021-9991 [doi]  [abs]
  70. Degond, P; Frouvelle, A; Liu, JG, Macroscopic limits and phase transition in a system of self-propelled particles, Journal of Nonlinear Science, vol. 23 no. 3 (June, 2013), pp. 427-456, Springer Nature, ISSN 0938-8974 [doi]  [abs]
  71. Chen, X; Liu, JG, Global weak entropy solution to Doi-Saintillan-Shelley model for active and passive rod-like and ellipsoidal particle suspensions, Journal of Differential Equations, vol. 254 no. 7 (April, 2013), pp. 2764-2802, Elsevier BV, ISSN 0022-0396 [doi]  [abs]
  72. Jin, S; Liu, JG; Wang, L, A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations, Mathematics of Computation, vol. 82 no. 282 (February, 2013), pp. 749-779, American Mathematical Society (AMS) [doi]  [abs]
  73. P. Degond, A. Frouvelle, J.-G. Liu, S Motsch, L Navoret, Macroscopic models of collective motion and self-organization, Seminaire Laurent Schwartz -- EDP et applicatios, vol. 2012 - 2013 (2013), pp. 1-27
  74. P. Degond, J.-G, Liu, S. Motsch, V. Panferov, Hydrodynamic models of self-organized dynamics: derivation and existence theory, Methods Anal. Appl., vol. 20 (2013), pp. 89-114
  75. Degond, P; Liu, J-G; 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. 1-30, Springer Nature, ISSN 0022-4715 [doi]  [abs]
  76. Chen, X; Jüngel, A; Liu, J-G, A Note on Aubin-Lions-Dubinskiǐ Lemmas, Acta Applicandae Mathematicae, vol. 133 no. 1 (2013), pp. 1-11, ISSN 0167-8019 [doi]  [abs]
  77. Degond, P; Liu, J-G; Ringhofer, C, Large-Scale Dynamics of Mean-Field Games Driven by Local Nash Equilibria, Journal of Nonlinear Science, vol. 24 no. 1 (2013), pp. 1-23, ISSN 0938-8974 [doi]  [abs]
  78. Chae, D; Degond, P; Liu, J-G, Well-posedness for Hall-magnetohydrodynamics, Annales De L'Institut Henri Poincare (C) Non Linear Analysis, vol. 31 no. 3 (2013), pp. 555-565, Elsevier BV, ISSN 0294-1449 [doi]  [abs]
  79. Haack, J; Jin, S; Liu, JG, An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equations, Communications in Computational Physics, vol. 12 no. 4 (October, 2012), pp. 955-980, Global Science Press, ISSN 1815-2406 [doi]  [abs]
  80. Chae, D; Liu, JG, Blow-up, Zero α Limit and the Liouville Type Theorem for the Euler-Poincaré Equations, Communications in Mathematical Physics, vol. 314 no. 3 (September, 2012), pp. 671-687, Springer Nature, ISSN 0010-3616 [doi]  [abs]
  81. Carrillo, JA; Chen, L; Liu, JG; Wang, J, A note on the subcritical two dimensional Keller-Segel system, Acta Applicandae Mathematicae, vol. 119 no. 1 (June, 2012), pp. 43-55, Springer Nature, ISSN 0167-8019 [doi]  [abs]
  82. Chen, L; Liu, JG; Wang, J, Multidimensional degenerate Keller-Segel system with critical diffusion exponent 2n/(n + 2), Siam Journal on Mathematical Analysis, vol. 44 no. 2 (May, 2012), pp. 1077-1102, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410 [doi]  [abs]
  83. 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. 791-826, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410 [doi]  [abs]
  84. 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. 1-21, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429 [doi]  [abs]
  85. Degond, P; Liu, JG, Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation, Mathematical Models and Methods in Applied Sciences, vol. 22 no. SUPPL.1 (April, 2012), pp. 1140001-1140001, World Scientific Pub Co Pte Lt, ISSN 0218-2025 [doi]  [abs]
  86. Chen, X; Liu, JG, Two nonlinear compactness theorems in Lp(0,T;B), Applied Mathematics Letters, vol. 25 no. 12 (January, 2012), pp. 2252-2257, Elsevier BV, ISSN 0893-9659 [doi]  [abs]
  87. A. Chertock, J.-G. Liu, and T. Pendleton, Convergence analysis of the particle method for the Camassa-Holm equation, in Proceedings of the 13th International Conference on ``Hyperbolic Problems: Theory, Numerics and Applications" (2012), pp. 365-373, Higher Education Press, Beijing
  88. Acheritogaray, M; Degond, P; Frouvelle, A; Liu, JG, Kinetic formulation and global existence for the hall-magneto-hydrodynamics system, Kinetic and Related Models, vol. 4 no. 4 (December, 2011), pp. 901-918, American Institute of Mathematical Sciences (AIMS), ISSN 1937-5093 [doi]  [abs]
  89. Zheng, W; Gao, H; Liu, JG; Zhang, Y; Ye, Q; Swank, C, General solution to gradient-induced transverse and longitudinal relaxation of spins undergoing restricted diffusion, Physical Review A, vol. 84 no. 5 (November, 2011), pp. 053411-8, American Physical Society (APS), ISSN 1050-2947 [doi]  [abs]
  90. Liu, JG; Lorz, A, A coupled chemotaxis-fluid model: Global existence, Annales De L'Institut Henri Poincare (C) Non Linear Analysis, vol. 28 no. 5 (January, 2011), pp. 643-652, Elsevier BV, ISSN 0294-1449 [doi]  [abs]
  91. 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. 649-667, Global Science Press, ISSN 1815-2406 [doi]  [abs]
  92. Liu, J-G; Pego, RL, STABLE DISCRETIZATION OF MAGNETOHYDRODYNAMICS IN BOUNDED DOMAINS, Communications in Mathematical Sciences, vol. 8 no. 1 (March, 2010), pp. 234-251, INT PRESS BOSTON, INC, ISSN 1539-6746  [abs]
  93. 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. 3428-3453, Elsevier BV, ISSN 0021-9991 [doi]  [abs]
  94. 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. 1474-1491, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429 [repository], [doi]  [abs]
  95. Liu, JG; Pego, RL, Stable discretization of magnetohydrodynamics in bounded domains, Communications in Mathematical Sciences, vol. 8 no. 1 (January, 2010), pp. 235-251, International Press of Boston, ISSN 1539-6746 [doi]  [abs]
  96. Liu, JG; Liu, J; Pego, RL, Error estimates for finite-element Navier-Stokes solvers without standard Inf-Sup conditions, Chinese Annals of Mathematics, Series B, vol. 30 no. 6 (December, 2009), pp. 743-768, Springer Nature, ISSN 0252-9599 [doi]  [abs]
  97. Liu, JG; Wang, WC, Characterization and regularity for axisymmetric solenoidal vector fields with application to navier-stokes equation, Siam Journal on Mathematical Analysis, vol. 41 no. 5 (December, 2009), pp. 1825-1850, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410 [doi]  [abs]
  98. Ha, SY; Liu, JG, A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, Communications in Mathematical Sciences, vol. 7 no. 2 (January, 2009), pp. 297-325, International Press of Boston, ISSN 1539-6746 [doi]  [abs]
  99. Degond, P; Liu, JG; Vignal, MH, Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit, Siam Journal on Numerical Analysis, vol. 46 no. 3 (November, 2008), pp. 1298-1322, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429 [doi]  [abs]
  100. Lin, P; Liu, JG; Lu, X, Long time numerical solution of the Navier-Stokes equations based on a sequential regularization formulation, Siam Journal on Scientific Computing, vol. 31 no. 1 (November, 2008), pp. 398-419, Society for Industrial & Applied Mathematics (SIAM), ISSN 1064-8275 [doi]  [abs]
  101. Lu, X; Lin, P; Liu, JG, Analysis of a sequential regularization method for the unsteady Navier-Stokes equations, Mathematics of Computation, vol. 77 no. 263 (July, 2008), pp. 1467-1494, American Mathematical Society (AMS), ISSN 0025-5718 [doi]  [abs]
  102. 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. 26-55, ISSN 1815-2406  [abs]
  103. Hsia, CH; Liu, JG; Wang, C, Structural stability and bifurcation for 2D incompressible ows with symmetry, Meth. Appl. Anal., vol. 15 (2008), pp. 495-512
  104. Antman, SS; Liu, JG, Basic themes and pretty problems of nonlinear solid mechanics, Milan Journal of Mathematics, vol. 75 no. 1 (December, 2007), pp. 135-176, Springer Nature, ISSN 1424-9286 [doi]  [abs]
  105. Moore, J; Cheng, Z; Hao, J; Guo, G; Liu, J-G; Lin, C; Yu, LL, 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, vol. 55 no. 25 (December, 2007), pp. 10173-10182, ISSN 0021-8561 (published on Web 10/30/2007.) [doi]  [abs]
  106. Liu, JG; Liu, J; Pego, RL, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, Communications on Pure and Applied Mathematics, vol. 60 no. 10 (October, 2007), pp. 1443-1487, WILEY, ISSN 0010-3640 [doi]  [abs]
  107. 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 Navier-Stokes equations and their Applications, edited by Y. Giga, H. Kozono, H. Okamoto and Y. Shibta (2007), pp. 251--270, Kyoto Univ.  [abs]
  108. Liu, JG; Liu, J; Pego, R, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate via a commutator estimate, Comm. Pure Appl. Math., vol. 60 (2007), pp. 1443-1487
  109. Degond, P; Jin, S; Liu, JG, Mach-number uniform asymptotic- preserving Gauge schemes for compressible flows, Bulletin of the Institute of Mathematics Academia Sinica (New Series), vol. 2 (2007), pp. 851-892  [abs]
  110. 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. 2456-2480, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429 [doi]  [abs]
  111. Degond, P; Liu, JG; Mieussens, L, Macroscopic fluid models with localized kinetic upscaling effects, Multiscale Modeling & Simulation, vol. 5 no. 3 (September, 2006), pp. 940-979, Society for Industrial & Applied Mathematics (SIAM), ISSN 1540-3459 [doi]  [abs]
  112. Moore, J; Liu, J-G; 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. 5313-5322, ISSN 0021-8561 [doi]  [abs]
  113. Liu, JG; Samelson, R; Wang, C, Global weak solution of planetary geostrophic equations with inviscid geostrophic balance, International Journal of Phytoremediation, vol. 85 no. 6-7 (January, 2006), pp. 593-605 [doi]  [abs]
  114. J.-G. Liu, Jie Liu and R. Pego, On incompressible Navier-Stokes 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. 29--44, Yokohama Publishers, Inc.
  115. Liu, JG; Wang, WC, Energy and helicity preserving schemes for hydro- and magnetohydro-dynamics flows with symmetry, Journal of Computational Physics, vol. 200 no. 1 (October, 2004), pp. 8-33, Elsevier BV [doi]  [abs]
  116. Ghil, M; Liu, JG; Wang, C; Wang, S, Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow, Physica D: Nonlinear Phenomena, vol. 197 no. 1-2 (October, 2004), pp. 149-173, Elsevier BV, ISSN 0167-2789 [doi]  [abs]
  117. 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. 429-451, Springer Nature, ISSN 0938-8974 [doi]  [abs]
  118. Johnston, H; Liu, JG, Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term, Journal of Computational Physics, vol. 199 no. 1 (September, 2004), pp. 221-259, Elsevier BV [doi]  [abs]
  119. 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. 267-290, American Institute of Mathematical Sciences (AIMS), ISSN 1534-0392 [doi]  [abs]
  120. 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. 555-594, Springer Nature [doi]  [abs]
  121. 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. 27-52, American Mathematical Society (AMS) [doi]  [abs]
  122. Liu, JG; Wang, C, High order finite difference methods for unsteady incompressible flows in multi-connected domains, Computers & Fluids, vol. 33 no. 2 (January, 2004), pp. 223-255, Elsevier BV [doi]  [abs]
  123. Li, B; Liu, JG, Eptaxial growth without slope selection: energetics, coarsening, and dynamic scaling, J. Nonlinear Sci., vol. 14 no. 5 (2004), pp. 429-451, ISSN 0938-8974 [doi]  [abs]
  124. Liu, JG; Wang, C, High order finite difference method for unsteady incompressible flow on multi-connected domain in vorticity-stream function formulation, Computer and Fluids, vol. 33 no. 2 (2004), pp. 223-255 [doi]  [abs]
  125. Li, B; Liu, JG, Thin film epitaxy with or without slope selection, European Journal of Applied Mathematics, vol. 14 no. 6 (December, 2003), pp. 713-743, Cambridge University Press (CUP) [doi]  [abs]
  126. Wang, C; Liu, JG, Positivity property of second-order flux-splitting schemes for the compressible Euler equations, Discrete and Continuous Dynamical Systems Series B, vol. 3 no. 2 (May, 2003), pp. 201-228, American Institute of Mathematical Sciences (AIMS) [doi]  [abs]
  127. 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. 253-285, ISSN 0885-7474 [doi]  [abs]
  128. Chainais-Hillairet, C; Liu, JG; Peng, YJ, Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis, Esaim: Mathematical Modelling and Numerical Analysis, vol. 37 no. 2 (January, 2003), pp. 319-338, E D P SCIENCES [doi]  [abs]
  129. Wang, C; Liu, JG, Fourth order convergence of a compact difference solver for incompressible flow, Commun. Appl. Anal., vol. 7 (2003), pp. 171-191
  130. Duraisamy, K; Baeder, JD; Liu, J-G, Concepts and Application of Time-Limiters to High Resolution Schemes, Journal of Scientific Computing, vol. 19 no. 1-3 (2003), pp. 139-162, ISSN 0885-7474 [doi]  [abs]
  131. Weinan, E; Liu, JG, Gauge method for viscous incompressible flows, Comm. Math. Sci., vol. 1 (2003), pp. 317-332
  132. Chern, IL; Liu, JG; Wang, WC, Accurate evaluation of electrostatics for macromolecules in solution, Methods and Applications of Analysis, vol. 10 (2003), pp. 309-328
  133. 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. 120-154, Elsevier BV, ISSN 0021-9991 [doi]  [abs]
  134. Wang, C; Liu, JG, Analysis of finite difference schemes for unsteady Navier-Stokes equations in vorticity formulation, Numerische Mathematik, vol. 91 no. 3 (May, 2002), pp. 543-576 [doi]  [abs]
  135. Weinan, E; Liu, JG, Projection method III: Spatial discretization on the staggered grid, Mathematics of Computation, vol. 71 no. 237 (January, 2002), pp. 27-47, American Mathematical Society (AMS) [doi]  [abs]
  136. Liu, JG; Wang, WC, An energy-preserving MAC-Yee scheme for the incompressible MHD equation, Journal of Computational Physics, vol. 174 no. 1 (November, 2001), pp. 12-37, Elsevier BV, ISSN 0021-9991 [doi]  [abs]
  137. Liu, JG; Xin, Z, Convergence of the point vortex method for 2-D vortex sheet, Mathematics of Computation, vol. 70 no. 234 (April, 2001), pp. 595-606, American Mathematical Society (AMS) [doi]  [abs]
  138. Liu, JG; Weinan, E, Simple finite element method in vorticity formulation for incompressible flows, Mathematics of Computation, vol. 70 no. 234 (April, 2001), pp. 579-593, American Mathematical Society (AMS) [doi]  [abs]
  139. Liu, JG; Weinan, E, Simple finite element method in vorticity formulation for incompressible flow, Math. Comp., vol. 69 (2001), pp. 1385-1407
  140. Liu, JG; Xin, Z, Convergence of point vortex method for 2-D vortex sheet, Math. Comp., vol. 70 no. 234 (2001), pp. 565-606 [doi]  [abs]
  141. 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. 701-710, WILEY, ISSN 0271-2091 [doi]  [abs]
  142. Wang, C; Liu, JG, Convergence of gauge method for incompressible flow, Mathematics of Computation, vol. 69 no. 232 (October, 2000), pp. 1385-1407  [abs]
  143. Liu, JG; Shu, CW, A High-Order Discontinuous Galerkin Method for 2D Incompressible Flows, Journal of Computational Physics, vol. 160 no. 2 (May, 2000), pp. 577-596, Elsevier BV [doi]  [abs]
  144. Liu, JG; Xin, Z, Convergence of a Galerkin method for 2-D discontinuous Euler flows, Communications on Pure and Applied Mathematics, vol. 53 no. 6 (January, 2000), pp. 786-798, WILEY [doi]  [abs]
  145. 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. 1025-1055  [abs]
  146. 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. 2446-2448 [doi]  [abs]
  147. 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. 237-256, Elsevier BV [doi]  [abs]
  148. Xu, E; Liu, JG, Pricing of mortgage-backed securities with option-adjusted spread, Managerial Finance, vol. 24 (1998), pp. 94-109
  149. E, W; Liu, JG, Finite Difference Methods for 3D Viscous Incompressible Flows in the Vorticity-Vector Potential Formulation on Nonstaggered Grids, Journal of Computational Physics, vol. 138 no. 1 (November, 1997), pp. 57-82, Elsevier BV [doi]  [abs]
  150. Chen, GQ; Liu, JG, Convergence of difference schemes with high resolution for conservation laws, Mathematics of Computation, vol. 66 no. 219 (July, 1997), pp. 1027-1053  [abs]
  151. 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. 67-76, Elsevier BV [doi]  [abs]
  152. Liu, JG; Xin, Z, Boundary-layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation, Archive for Rational Mechanics and Analysis, vol. 135 no. 1 (October, 1996), pp. 61-105, Springer Nature [doi]  [abs]
  153. Weinan, E; Liu, JG, Projection method II: Godunov-Ryabenki analysis, Siam Journal on Numerical Analysis, vol. 33 no. 4 (August, 1996), pp. 1597-1621, Society for Industrial & Applied Mathematics (SIAM) [doi]  [abs]
  154. 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. 368-382, Elsevier BV [doi]  [abs]
  155. Jin, S; Liu, JG, The effects of numerical viscosities: I. Slowly moving shocks, Journal of Computational Physics, vol. 126 no. 2 (January, 1996), pp. 373-389, Elsevier BV [doi]  [abs]
  156. Weinan, E; Liu, JG, Essentially compact schemes for unsteady viscous incompressible flows, Journal of Computational Physics, vol. 126 no. 1 (January, 1996), pp. 122-138, Elsevier BV [doi]  [abs]
  157. Levermore, CD; Liu, JG, Large oscillations arising in a dispersive numerical scheme, Physica D: Nonlinear Phenomena, vol. 99 no. 2-3 (January, 1996), pp. 191-216, Elsevier BV [doi]  [abs]
  158. Liu, JG; Xin, Z, Kinetic and viscous boundary layers for broadwell equations, Transport Theory and Statistical Physics, vol. 25 no. 3-5 (January, 1996), pp. 447-461, Informa UK Limited [doi]  [abs]
  159. Jin, S; Liu, JG, Oscillations induced by numerical viscosities, Mat. Contemp., vol. 10 (1996), pp. 169-180
  160. 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. 611-628 [doi]  [abs]
  161. Weinan, E; Liu, JG, Projection method I: convergence and numerical boundary layers, Siam J. Numer. Anal., vol. 32 (1995), pp. 1017-1057
  162. 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. 555-563  [abs]
  163. Lefloch, P; Liu, JG, Discrete entropy and monotonicity criteria for hyperbolic conservation laws, C.R. Acad. Sci. Paris., vol. 319 (1994), pp. 881-886
  164. 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. 217-256, Springer Nature, ISSN 0003-9527 [doi]  [abs]
  165. Chen, GQ; Liu, JG, Convergence of second-order schemes for isentropic gas dynamics, Mathematics of Computation, vol. 61 no. 204 (January, 1993), pp. 607-627, American Mathematical Society (AMS) [doi]  [abs]
  166. 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. 1327-1361, WILEY [doi]  [abs]
  167. Liu, JG; Xin, Z, L1-stability of stationary discrete shocks, Mathematics of Computation, vol. 60 no. 201 (January, 1993), pp. 233-244, American Mathematical Society (AMS) [doi]  [abs]

Papers Accepted

  1. P. Degond, J.-G. Liu, S. Merino-Aceituno, T. Tardiveau, Continuum dynamics of the intention field under weakly cohesive social interactions, Math. Models Methods Appl. Sci. (2016)
  2. 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
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320