Publications of Chun Liu

Here is the list the postScript files for some of my recent publications. Please e-mail me if you would like to have the hard copy or the electronic files of the papers which are not available here. The list of my publications and their BIBTEX entries can also be found in MathSciNet (license to MathSciNet is required).

Selected Publications

(with Fang-Hua Lin) Nonlinear Dissipative Systems Modeling the Flow of Liquid Crystals . Comm. Pure. Appl. Math., Vol. XLVIII, 501--537 (1995)
(with Fang-Hua Lin) Partial Regularities of the Nonlinear Dissipative Systems Modeling the Flow of Liquid Crystals. Discrete and Continuous Dynamic Systems, Vol 2, No 1, 1--23 (1996)
(with David Kinderlehrer) Revisiting the Focal Conic Structures in Smectic A . Proc. Symposium on Elasticity to honor Professor J.L.~Ericksen. ASME Mechanics and Materials Conference (1996)
(with Sergio A.~Alvarez) Motion of a closed interface by minus the surface Laplacian of Curvature . Differential and Integral Equations, Vol 13, No. 10-12, 1583--1594 (1997)
(with Noel J.~Walkington) Approximation of Liquid Crystal Flows. SIAM Journal of Numerical Analysis, Vol 37, 725--738 (2000)
(with M.~Carme Calderer and Karl Voss) Radial Configurations of Smectic A materials and Focal Conics . Physica D, Vol 124, 11--22 (1998)
(with Fang-Hua Lin) Existence of Solutions for Ericksen-Leslie System. Arch. Ration. Mech. Anal. 154 (2000), no. 2, 135--156.
(with M.~Carme Calderer) Liquid Crystal Poiseuille Flow: Dynamic and Static Configurations. SIAM Journal of Applied Mathematics, Vol 60, No 6, 1925--1949 (2000)
(with David Kinderlehrer, Florin Manolache and Shlomo Ta'asan) Remarks about Analysis and Simulation of Grain Boundary Systems. Proc. of Third International Conference of Grain Growth, 437--443 (1998)
The Dynamic for Incompressible Smectic~A Liquid Crystals: Existence and Regularity. Discrete and Continuous Dynamic Systems, Vol 6, No 3, 591--608 (2000)
(with M.~Carme Calderer) Poiseuille Flow of Nematic Liquid Crystals. International Journal of Engineering, Vol 38, 1007--1022 (2000)
(with M.~Carme Calderer) Mathematical Developments in the Study of Smectic A Liquid Crystals. International Journal of Engineering, Vol 38, 1113--1128 (2000)
(with David Kinderlehrer) Evolution of Grain Boundaries . To appear in Math. Mod. Meth. Appl. Sci. (1999)
(with M.~Carme Calderer and Karl Voss) Smectic~A Liquid Crystal Configurations with Interface Defects . To appear in Math. Methods. Appl. Sci. (1999)
(with M.~Carme Calderer and Quan Shen) Axisymmetric Configurations of Bipolar Liquid Crystal Droplets. Continuum Mechanics and Thermodynamics 14(4), 363-375 (2002).
The Stability of the Radial Solution of the Ginzburg-Landau Equation with Magnetic Fields. (1997)
(with M.~Carme Calderer, Dmitry Golovaty and Fanghua Lin) Time Evolution of Nematic Liquid Crystals with Variable Degree of Orientation. SIAM Jour. of Math. Ana., Vol 33, No. 5, 1033--1047 (1999)
(with Noel J.~Walkington) Mixed Method for the Approximation of Liquid Crystal Flows . M2AN, Vol. 36, No.2, pp. 205-222 (2002).
(with Jie Shen) On Liquid Crystal Flows with Free-Slip Boundary Conditions. Discrete and Continuous Dynamic Systems, Vol 7, No. 2, 307--318 (2001)
(with Noel J. Walkington) An Eulerian Description of Fluids Containing Visco-hyperelastic Particles. Arch. Ration. Mech. Anal. 159, 229 -- 252 (2001).
(with R. Buerger and W.L. Wendland) Existence and stability for mathematical models of sedimentation-consolidation processes in several space dimensions. Journal of Math. Anal. Appl., 264, 288-310 (2001)
(with Fanghua Lin) Static and Dynamic Theories of Liquid Crystals. Journal of Partial Differential Equations 14, no. 4, 289--330 (2001).
(with Q. Wang, W. E and P. Zhang) A Kinetic theory for flows of nonhomogeneous rodlike liquid crystalline polymers with a nonlocal intermolecular potential. Phys. Rev. E 65, 051504 (2002).
(with Patricia Bauman, M. Carme Calderer and Daniel Phillips) The Phase transition between chiral nematic and smectic~A* liquid crystals. Arch. Ration. Mech. Anal. 165, 2, 161-186 (2002)
(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)
(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).
(with Mingjun Lai and Paul Wenston) On Two Nonlinear Biharmonic Evolution Equations: Existence, Uniqueness and Stability . Appl. Anal. 83 (2004), no. 6, 541--562.
(with Mingjun Lai and Paul Wenston) Numerical Simulations on Two Nonlinear Biharmonic Evolution Equations . Appl. Anal. 83 (2004), no. 6, 563--577.
(with Noel J. Walkington) Convergence of Numerical Approximations of the Incompressible Navier Stokes Equations with Variable Density and Viscosity. Submitted to SINUM (2002).
(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, Vol 198, No. 2, 450--468 (2004).
(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).
(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 Modeling and Simulation , Vol 3, No 4, 895 --- 917 (2005).
(with Qiang Du and Xiaoqiang Wang) Retrieving Topological Information For Phase Field Models. SIAM Journal on Applied Mathematics, Volume 65, Number 6 pp. 1913-1932 (2005).
(with Fanghua Lin and Ping Zhang) On Hydrodynamics of Viscoelastic Fluids. Comm. Pure Appl. Math., Vol LVIII, 1 --- 35 (2005).
(with Qiang Du, Rolf Ryham and Xiaoqiang Wang) The Phase Field Formulation of the Willmore Problem. Nonlinearity 18, 1249 -- 1267 (2005).
(with Qiang Du, Rolf Ryham and Xiaoqiang Wang) Modeling the spontaneous curvature effects in tatic cell membrane deformation by a phase feld formulation. Communications in Pure and Applied Analysis, Volume 4, Number 3, 537 - 548(2005).
(with Fanghua Lin and Ping Zhang) On a Micro-Macro Model for Polymeric Fluids near Equilibrium. Submitted for publication (2004).
(with Peng Yu and Qiang Du) FENE dumbbell model and its several linear and nonlinear closure approximations. SIAM Journal on Multiscale Modeling and Simulation Volume 4, Number 3 pp. 709-731 (2005).
(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).
(with Pengtao Yue, Jimmy Feng and Jie Shen) Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid . Journal of Colloid and Interface Science Volume 290, Issue 1 , Pages 281-288 (2005).
(with Pengtao Yue, Jimmy Feng and Jie Shen) Viscoelastic effects on drop deformation in steady shear. J. Fluid Mech. 540, 427-437 (2005).
(with Zhen Lei and Yi Zhou) Global Solutions for Incompressible Viscoelastic Fluids. Arch. Rational Mech. Anal. 188 (2008) 371 -- 398.
(with Zhen Lei and Yi Zhou) GLOBAL EXISTENCE FOR A 2D INCOMPRESSIBLE VISCOELASTIC MODEL WITH SMALL STRAIN. COMMUN. MATH. SCI., Vol. 5, No. 3 (2007) pp. 595 --- 616.
(with Hailiang Liu) Boundary Conditions for the Microscopic FENE Models. SIAP Volume 68 Issue 5 (2008) Pages 1304-1315.

Last modified August 31, 2005

Chun Liu (liu@math.psu.edu)