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

Books

  1. Dynamics in Models of Coarsening, Coagulation, Condensation and Quantization, edited by W. Bao and J.-G. Liu (2007), World Scientific, ISBN 9789812708502
  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. 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

Papers Published

  1. 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]
  2. 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]
  3. 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]
  4. 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]
  5. 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 (July, 2008), pp. 26-55, ISSN 1815-2406  [abs]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. 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]
  11. Johnston, H; Wang, C; Liu, J-G, A Local Pressure Boundary Condition Spectral Collocation Scheme for the Three-Dimensional Navier–Stokes Equations, Journal of Scientific Computing, vol. 60 no. 3 (2014), pp. 612-626, Springer Nature, ISSN 0885-7474 [doi]  [abs]
  12. 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]
  13. 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]
  14. 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]
  15. 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]
  16. 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]
  17. 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
  18. 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]
  19. 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]
  20. 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]
  21. 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]
  22. 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
  23. 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]
  24. 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]
  25. 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]
  26. 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]
  27. 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]
  28. Huang, YL; Liu, JG; Wang, WC, An FFT based fast poisson solver on spherical shells, Communications in Computational Physics, vol. 9 no. 3 (March, 2011), pp. 649-667, Global Science Press, ISSN 1815-2406 [doi]  [abs]
  29. 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]
  30. 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]
  31. 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]
  32. 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]
  33. 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]
  34. 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]
  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. 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]
  37. 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]
  38. 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]
  39. 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]
  40. 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]
  41. 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]
  42. 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]
  43. 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]
  44. 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]
  45. 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]
  46. 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]
  47. 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]
  48. 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]
  49. 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]
  50. 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]
  51. 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]
  52. 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]
  53. 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
  54. 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]
  55. 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]
  56. 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]
  57. 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]
  58. 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]
  59. Wang, C; Liu, JG, Convergence of gauge method for incompressible flow, Mathematics of Computation, vol. 69 no. 232 (October, 2000), pp. 1385-1407  [abs]
  60. 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]
  61. 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]
  62. 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
  63. 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]
  64. 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]
  65. Lefloch, P; Liu, JG, Discrete entropy and monotonicity criteria for hyperbolic conservation laws, C.R. Acad. Sci. Paris., vol. 319 (1994), pp. 881-886
  66. 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]
  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 (2013), pp. 1-54, Springer Nature, ISSN 0010-3616 [doi]  [abs]
  68. 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]
  69. 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]
  70. 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]
  71. 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]
  72. Chertock, A; Liu, J-G; Pendleton, T, Elastic collisions among peakon solutions for the Camassa-Holm equation, Applied Numerical Mathematics, vol. 93 (2014), pp. 30-46, Elsevier BV, ISSN 0168-9274 [doi]  [abs]
  73. 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]
  74. 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]
  75. 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]
  76. 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]
  77. 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]
  78. 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]
  79. 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
  80. 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]
  81. 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]
  82. 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]
  83. 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]
  84. 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]
  85. 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]
  86. 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]
  87. 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]
  88. 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]
  89. 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]
  90. 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]
  91. 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]
  92. 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]
  93. 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]
  94. 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]
  95. 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]
  96. Wang, C; Liu, JG, Fourth order convergence of a compact difference solver for incompressible flow, Commun. Appl. Anal., vol. 7 (2003), pp. 171-191
  97. 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]
  98. 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]
  99. Weinan, E; Liu, JG, Gauge method for viscous incompressible flows, Comm. Math. Sci., vol. 1 (2003), pp. 317-332
  100. 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]
  101. 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]
  102. 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]
  103. 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]
  104. 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]
  105. 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]
  106. 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]
  107. 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]
  108. 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]
  109. 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
  110. 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]
  111. 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]
  112. 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]
  113. 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]
  114. 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]
  115. 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]
  116. 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]
  117. 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]
  118. 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]
  119. 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]
  120. 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]
  121. 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 (2013), pp. 427-456 [doi]  [abs]
  122. 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
  123. 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]
  124. 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]
  125. 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]
  126. 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]
  127. 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]
  128. 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]
  129. 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]
  130. 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.
  131. 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]
  132. Jin, S; Liu, JG, Oscillations induced by numerical viscosities, Mat. Contemp., vol. 10 (1996), pp. 169-180
  133. 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]
  134. 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]
  135. 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]
  136. Degond, P; Frouvelle, A; Liu, J-G, Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics, Archive for Rational Mechanics and Analysis, vol. 216 no. 1 (October, 2014), pp. 63-115, Springer New York LLC, ISSN 0003-9527 [doi]  [abs]
  137. 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]
  138. 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]
  139. Xu, E; Liu, JG, Pricing of mortgage-backed securities with option-adjusted spread, Managerial Finance, vol. 24 (1998), pp. 94-109
  140. Weinan, E; Liu, JG, Projection method I: convergence and numerical boundary layers, Siam J. Numer. Anal., vol. 32 (1995), pp. 1017-1057
  141. 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]
  142. 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]
  143. 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)
  144. 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]
  145. 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 (1994), pp. 555-563  [abs]
  146. 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]
  147. Liu, JG; Weinan, E, Simple finite element method in vorticity formulation for incompressible flow, Math. Comp., vol. 69 (2001), pp. 1385-1407
  148. 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]
  149. 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]
  150. 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]
  151. 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]
  152. 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
  153. Liu, JG; Liu, J; Pego, RL, Stable and accurate pressure approximation for unsteady incompressible viscous flow, Journal of Computational Physics, vol. 229 no. 9 (May, 2010), pp. 3428-3453, Elsevier BV, ISSN 0021-9991 [doi]  [abs]
  154. 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]
  155. 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]
  156. 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
  157. 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]
  158. 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]
  159. 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]
  160. 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]
  161. 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]
  162. 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]
  163. 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]
  164. 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]
  165. 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]
  166. 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]
  167. 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]
  168. 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]
  169. 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]

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)

 

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