PUBLICATION LIST

Chun Liu
September 20, 2011

Appeared:

  1. (with Fang-Hua Lin) Nonparabolic Dissipative Systems Modeling the Flow of Liquid Crystals, Communications on Pure and Applied Mathematics, Vol. 48, Issue 5, 501 – 537 (1995). abstract
  2. (with Fang-Hua Lin) Partial Regularity of the Dynamic System Modeling the Flow of Liquid Crystals, Discrete and Continuous Dynamic Systems, Vol 2, No 1, 1 – 23 (1996). abstract
  3. (with David Kinderlehrer) Revisiting the Focal Conic Structures in Smectic A, Proceeding of Symposium on Elasticity to honor Professor J.L. Ericksen. ASME Mechanics and Materials Conference, 217 – 225 (1996).
  4. (with Sergio A. Alvarez) Motion of a Closed Curve by Minus the Surface Laplacian of Curvature, Differential and Integral Equations, Vol 13, No. 10-12, 1583–1594 (1997).
  5. (with David Kinderlehrer, Florin Manolache and Shlomo Ta’asan) Remarks about Analysis and Simulation of Grain Boundary Systems, Proceeding of Third International Conference of Grain Growth, 437 – 443 (1998).
  6. (with M. Carme Calderer and Karl Voss) Radial Configurations of Smectic A materials and Focal Conics, Physica D, 124, 11—22 (1998). abstract
  7. (with Noel J. Walkington) Approximation of Liquid Crystal Flows, Siam Journal of Numerical Analysis, Vol 37, 725–741 (2000). abstract
  8. (with Fang-Hua Lin) Existence of Solutions for Ericksen-Leslie System, Archive for Rational Mechanics and Analysis, 154, no. 2, 135–156 (2000). abstract
  9. (with M. Carme Calderer) Liquid Crystal Flow: Dynamic and Static Configurations, Siam Journal of Applied Mathematics 60 (6), 1925 – 1949 (2000). abstract
  10. Dynamic Theory for Incompressible Smectic-A Liquid Crystals: Existence and Regularity, Discrete and Continuous Dynamic Systems, Vol 6, Num. 3, 591–608 (2000). abstract
  11. (with M. Carme Calderer) Poiseuille Flow of Nematic Liquid Crystals, International Journal of Engineering Science, 38, 1007-1022 (2000). abstract
  12. (with M. Carme Calderer) Mathematical Developments in the Study of Smectic A Liquid Crystals, International Journal of Engineering Science, 38, 1113-1128 (2000). abstract
  13. (with David Kinderlehrer) Evolution of Grain Boundaries, Mathematical Models and Methods in Applied Sciences (M3AS), 11 (4) , 713–729 (2001). abstract
  14. (with M. Carme Calderer and Karl Voss) Smectic A Liquid Crystal Configurations with Interface Defects, Mathematical Methods in the Applied Sciences, 24 (7), 473–489 (2001). abstract
  15. (with Jie Shen) On Liquid Crystal Flows with Free-Slip Boundary Conditions, Discrete and Continuous Dynamic Systems, Vol 7, No. 2, 307–318 (2001). abstract
  16. (with Noel J. Walkington) An Eulerian Description of Fluids Containing Visco-Elastic Particles, Archive for Rational Mechanics and Analysis, 159, 229–252 (2001). abstract
  17. (with M. Carme Calderer, Dmitry Golovaty and Fanghua Lin) Time Evolution of Nematic Liquid Crystals with Variable Degree of Orientation, SIAM Journal on Mathematical Analysis, 33 (5), 1033–1047 (2001). abstract
  18. (with Raimund Burger and Wolfgang Wendland) Existence and Stability for Mathematical Models of Sedimentation-Consolidation Processes in Several Space Dimensions, Journal of Mathematical Analysis and Applications, 264, 288–310 (2001). abstract
  19. (with Fanghua Lin) Static and Dynamic Theories of Liquid Crystals, Journal of Partial Differential Equations, Vol 14, No. 4, 289–330 (2001). article
  20. (with Qi Wang, Weinan E and Pingwen Wang) Kinetic theory for flows of nonhomogeneous rodlike liquid crystalline polymers with a nonlocal intermolecular potential, Physical Review E, 65, 051504 (2002). abstract
  21. (with Noel J. Walkington) Mixed Method for the Approximation of Liquid Crystal Flows, Mathematical Modelling and Numerical Analysis, Vol. 36, No. 2, pp. 205-222 (2002). abstract
  22. (with M. Carme Calderer and Quan Shen) Axisymmetric Configurations of Bipolar Liquid Crystal Droplets, Continuum Mechanics and Thermodynamics, Vol 14, No. 4, 363–375 (2002). abstract
  23. (with Bagisa Mukherjee) On Stability of Two Nematic Liquid Crystal Configurations, Discrete and Continuous Dynamic Systems B, Vol 2, No. 4, 561 –574 (2002). abstract
  24. (with Patricia Bauman, M. Carme Calderer and Daniel Phillips) The Phase Transition Between Chiral Nematic and Smectic A* Liquid Crystals, Archive for Rational Mechanics and Analysis, 165, 2, 161 – 186 (2002). abstract
  25. (with Jie Shen) A Phase Field Model for the Mixture of Two Incompressible Fluids and its Approximation by a Fourier-Spectral Method, Physica D, 179, 4, 211–228 (2003). abstract
  26. (with Mingjun Lai and Paul Wenston) Bivariate Spline Method for Numerical Solution of Time Evolution Navier-Stokes Equations Over Polygons in Stream Function Formulation, Numerical Methods for Partial Differential Equations, Vol. 19, No. 6, 776–827 (2003). abstract
  27. (with Mingjun Lai and Paul Wenston) Numerical Simulations on Two Nonlinear Biharmonic Evolution Equations, Applicable Analysis 83, no. 6, 563–577 (2004). abstract
  28. (with Qiang Du and Xiaoqiang Wang) A Phase Field Approach in the Numerical Study of the Elastic Bending Energy for Vesicle Membranes, Journal of Computational Physics 198, no. 2, 450–468 (2004). abstract
  29. (with Pengtao Yue, Jimmy Feng and Jie Shen) A Diffuse-Interface Method for Simulating Two-Phase Flows of Complex Fluids, Journal of Fluid Mechanics, Vol 515, 293–317 (2004). abstract
  30. (with Fanghua Lin and Ping Zhang) On Hydrodynamics of Viscoelastic Fluids, Communication of Pure and Applied Mathematics, Vol 58, Issue 11, 1437 — 1471 (2005). abstract
  31. (with Qiang Du, Rolf Ryham and Xiaoqiang Wang) A Phase Field Formulation of the Willmore Problem, Nonlinearity, 18, 1249 — 1267 (2005). abstract
  32. (with Peng Yu and Qiang Du) From Micro to Macro Dynamics Via a New Closure Approximation to the FENE Model of Polymeric Fluids, SIAM Journal on Multiscale Modelling and Simulation, Vol 3, No 4, 895 — 917 (2005). abstract
  33. (with Qiang Du, Rolf Ryham and Xiaoqiang Wang) Modeling the spontaneous curvature effects in static cell membrane deformation by a phase field formulation, Communications in Pure and Applied Analysis, Vol 4, No 3, 537 — 548 (2005). abstract
  34. (with Qiang Du and Xiaoqiang Wang) Retrieving Topological Information For Phase Field Models, SIAM Journal on Applied Mathematics, Vol 65, No 6, 1913 — 1932 (2005). abstract
  35. (with Pengtao Yue, Jimmy Feng and Jie Shen) Interfacial Forces and Marangoni Flow on a Nematic Drop, Journal of Colloid and Interface Science, 290, 281 — 288 (2005). abstract
  36. (with Qiang Du and Peng Yu) FENE dumbbell model and its several linear and nonlinear closure approximations, SIAM Journal on Multiscale Modeling and Simulation, Vol 4, No 3, 709 — 731 (2005). abstract
  37. (with Pengtao Yue, Jimmy Feng and Jie Shen) Diffuse-Interface Simulations of Drop-Coalescence and Retraction in Viscoelastic Fluids, Journal of Non-Newtonian Fluid Dynamics, Vol 129, 163 — 176 (2005). abstract
  38. (with Pengtao Yue, Jimmy Feng and Jie Shen) Viscoelastic Effects on Drop Deformation in Steady Shear, Journal of Fluid Mechanics, 540, 427 — 437(2005). abstract
  39. (with Qiang Du and Xiaoqiang Wang) Simulating the Deformation of Vesicle Membranes under Elastic Bending Energy in Three Dimensions, Journal of Computational Physics, 212, 2, 757 — 777 (2006). abstract
  40. (with Pengtao Yue, Jimmy Feng and Jie Shen) Transient drop deformation upon startup of shear in viscoelastic fluids, Physics of Fluids, 17, 123101 (2005). abstract
  41. (with Rolf Ryham and Zhiqiang Wang) On Electro-Kinetic Fluids: One Dimensional Configurations, Discrete and Continuous Dynamical Systems B, Volume 6, Number 2, 357 — 371 (2006). abstract
  42. (with Pengtao Yue, Jimmy Feng and Jie Shen) Variational Approach in Two-Phase Flows of Complex Fluids transport and induced elastic stress, in A. Miranville, editor, Mathematical Models and Methods in Phase Transitions,. Nova Publications, (2005). (21 pages)
  43. (with Pengtao Yue, Jimmy Feng and Jie Shen) An Energetic Variational Formulation with Phase Field Methods for Interfacial Dynamics of Complex Fluids: Advantages and Challenges, in M.C. Calderer, E. Terentjev editors, ”Modeling of Soft Matter”, IMA Volumes in Mathematics and its Applications, Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN (2005). (29 pages)
  44. (with Fanghua Lin and Ping Zhang) On a Micro-Macro Model for Polymeric Fluids near Equilibrium, Communications on Pure and Applied Mathematics, Vol 60. Issue 6, 838—866 (2007). abstract
  45. (with Ping Lin) Simulations of singularity dynamics in liquid crystal flows: a fast C0 Finite element approach, Journal of Computational Physics, 215 (1), 348–362 (2006). abstract
  46. (with Carme Calderer and Baisheng Yan) A model for total energy of nematic elastomers with non-uniform prolate spheroids. Advances in applied and computational mathematics, Advances in applied and computational mathematics, 245–259, Nova Sci. Publ., Hauppauge, NY, (2006).
  47. (with Xiaofeng Yang, Jimmy Feng and Jie Shen) Numerical Simulations of Jet Pinching-off and Drop Formation using an Energetic Variational Phase-Field Method, Journal of Computational Physics 218:417-428 (2006). abstract
  48. (with C. Zhou, P. Yue, J Feng and Jie Shen) Heart-shaped bubbles rising in anisotropic liquids, Physics of Fluids, 19, 041703 (2007). abstract
  49. (with Qiang Du, Rolf Ryham and Xiaoqiang Wang) Diffusive Interface Energies Capturing the Euler Number: Relaxation and Renormalization, Communications of Mathematical Sciences 5, pp.233-242 (2007). article
  50. (with Xiaobing Feng and Yinnian He) Analysis of finite element approximations of a phase field model for two phase fluids, Mathematics of Computation 76, no. 258, 539–571 (2007). abstract
  51. (with Noel J. Walkington) Convergence of Numerical Approximations of the Incompressible Navier Stokes Equations with Variable Density and Viscosity, SIAM Journal of Numerical Analysis 45, no. 3, 1287–1304 (2007). abstract
  52. (with Qiang Du and Manlin Li) Analysis of a Phase Field Navier-Stokes Vesicle-Fluid Interaction Model, Discrete and Continuous Dynamical Systems B, 8, No 3, pp.539-556, (2007). abstract
  53. (with Zhen Lei and Yi Zhou) Global Existence for Small Strain Viscoelasticity, Communication in Mathematical Sciences 5, No 3, 595 — 616 (2007). article
  54. (with Rolf Ryham and Ludmil Zikatanov) Mathematical Models for the Deformation of Electrolyte Droplets, Discrete and Continuous Dynamical Systems B, Volume 8, Number 3, 649 — 661 (2007). abstract
  55. (with Ping Lin and Hui Zhang) An energy law preserving C0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics, Journal of Computational Physics, Volume 227, Issue 2, 1411 —1427 (2007). abstract
  56. (with Zhen Lei and Yi Zhou) Global Solutions for Incompressible Viscoelastic Fluids, Archive for Rational Mechanics and Analysis 188, 371 – 398 (2008). abstract
  57. (with Hailiang Liu) Boundary Conditions for the Microscopic FENE Models, SIAM Journal of Applied Mathematics Volume 68, Issue 5, 1304—1315 (2008). abstract
  58. (with Yunkyong Hyon, Jose A. Carrillo and Qiang Du) A Macroscopic Closure Approximation to the Micro-Macro FENE Models with Maximum Entropy Principle for Polymeric Materials, Kinetic and Related Models, Volume 1, Number 2, 171 — 184 (2008). abstract
  59. (with Aaron Naber, Jimmy Feng and Christopher A. Bertelo) The Nucleation and Growth of Gas Bubbles in a Newtonian Fluid: An Energetic Variational Phase Field Approach, in Moving Interface Problems and Applications in Fluid Dynamics (AMS Contemporary Mathematics Series, Vol. 466, eds. K. B. Cheong, Z. Li and P. Lin). pp. 95-120. American Mathematics Society (2008).
  60. (with Yunkyong Hyon and Qiang Du) An Enhanced Macroscopic Closure Approximation to the Micro-macro FENE Models for Polymeric Materials, SIAM Journal of Multiscale Modeling and Simulation, Volume 7, Number 2, 978 — 1002 (2008). abstract
  61. (with Jianwei Zhang, Xiuqing Gong, Weijia Wen and Ping Sheng) Electrorheological Fluid Dynamics, Physical Review Letters 101, 194503 (2008). abstract
  62. (with Huan Sun) On Energetic Variational Approaches in Modeling the Nematic Liquid Crystal Flows, Discrete and Continuous Dynamical Systems, Volume 23, Number 2, 455 — 475 (2009). abstract
  63. (with Qiang Du, Rolf Ryham and Xiaoqiang Wang) Energetic Variational Approaches to Modeling Vesicle and Fluid Interactions, Physica D, 238, 923—930 (2009). abstract
  64. (with Pengtao Sun and Jinchao Xu) Phase Field Model of Thermo-Induced Marangoni Effects in the Mixtures and its Numerical Simulations with Mixed Finite Element Methods, Communications in Computational Physics, 6, 1095 — 1117(2009). abstract
  65. (with Yunkyong Hyon and Do Young Kwak) Energetic Variational Approach in Complex Fluids : Maximum Dissipation Principle, Discrete and Continuous Dynamical Systems, Volume 26, Number 4, 1291 — 1304 (2010). abstract
  66. (with Xiang Xu and Liyun Zhao) Axisymmetric Solutions to a coupled Navier-Stokes/Allen-Cahn Equations, SIAM Journal of Mathematical Analysis, Volume 41, Issue 6, 2246-2282 (2010). abstract
  67. (with Qiang Du and Yunkyong Hyon) On some PDF based moment closure approximations of micro-macro models for viscoelastic polymeric fluids, Journal of Computational and Theoretical Nanoscience, 7, 738 — 755 (2010). abstract
  68. (with Norifumi Sato and Yoshihiro Tonegawa) On the Existence of Mean Curvature Flow with Transport Term, Interfaces and Free Boundaries 12, No 2, 251-277 (2010). abstract
  69. (with Huan Sun) The Slip Boundary Condition in the Dynamics of Solid Particles Immersed in Stokesian Flows, Solid State Communications, Volume 150, Issues 22, 990-1002 (2010). abstract
  70. (with Yunkyong Hyon and Robert Eisenberg) Energy Variational Analysis EnVarA of Ions in Water and Channels: Field Theory for Primitive Models of Complex Ionic Fluids, Journal of Chemical Physics 133, 104104 (2010) . abstract
  71. (with Shupeng Zhang and Hui Zhang) Numerical Simulations of Hydrodynamics of Nematic Liquid Crystals: Effects of Kinematic Transports, Communications in Computational Physics Vol. 9, No. 4, 974-993 (2010). abstract
  72. (with Yunkyong Hyon and Robert Eisenberg) A Mathematical Model for the Hard Sphere Repulsion in Ionic Solutions, Communications in Mathematical Sciences 9(2), pp.459–475, 2011. article
  73. (with Chiun-Chang Lee, Hijin Lee, Yunkyong Hyon and Taichia Lin) New Poisson-Boltzmann Type Equations: One-Dimensional Solutions, Nonlinearity 24, pp.431–458, 2011. abstract
  74. (with Jinsong Hua, Ping Lin and Qi Wang) Energy Law Preserving C0 Finite Element Schemes for Phase Field Models in Two-Phase Flow Computations, Journal of Computational Physics 230, 7115 – 7131 (2011). abstract
  75. (with James H. Adler, James Brannick, Thomas Manteuffel and Ludmil Zikatanov) First-order system least squares and the energetic variational approach for two-phase flow, Journal of Computational Physics 230(17):6647-6663 (2011). abstract
  76. (with Xiaofeng Yang, M. Gregory Forest and Jie Shen) Shear Cell Rupture of Nematic Droplets in Viscous Fluids, Journal of Non-Newtonian Fluid Mechanics 166:487499 (2011). abstract

To Appear:

  1. (with Yoichiro Mori and Robert S. Eisenberg) A Model of Electrodiffusion and Osmotic Water Flow and its Energetic Structure, to appear in Physica D (2011). (49 pages) abstract
  2. (with Yunkyong Hyon, James E. Fonseca and Robert Eisenberg) Energy Variational Approach To Study Charge Inversion (Layering) Near Charged Wall, to appear in Discrete and Continuous Dynamical Systems (2010). (22 pages)

Other Publications:

  1. Variational Approaches in Complex Fluids, Lecture Notes (2004).
  2. Multi-scale Phenomena in Complex Fluids: Modeling, Analysis and Numerical Simulations (Series in Contemporary Applied Mathematics) (Series in Contemporary Applied Mathematics Cam) by Thomas Y. Hou (Author, Editor), Chun Liu (Editor), Jian-guo Liu (Editor), World Scientific Publishing Company ( 2009). abstract and contents
  3. Nonlinear Conservation Laws, Fluid Systems and Related Topics (Series in Contemporary Applied Mathematics) by Gui-Qiang Chen (Author, Editor), Ta-Tsien Li (Editor), Chun Liu (Editor), World Scientific Publishing Company ( 2009). abstract and contents
  4. Energetic Variational Approaches for Complex Fluids. Proceeding of the 36th Sapporo Symposium on Partial Differential Equations, August 22 - 24, 2011, Faculty of Science, Hokkaido University (2011). abstract