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GLOBAL EXISTENCE AND long-time behavior FOR THE STRONG SOLUTIONS IN H2 TO THE 3D COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS

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Annals of Applied Mathematics 2016年第4期32卷 331-356页

作者： Jincheng Gao Boling Guo Xiaoyu Xi Institute of Applied Physics and Computational Math. 100088BeijingPR China Graduate School of China Academy of Engineering Physics 100088BeijingPR China

In this paper, we investigate the global existence and long time behavior of strong solutions for compressible nematic liquid crystal flows in threedimensional whole space. The global existence of strong solutions is obtained by the standard energy method under the condition that the initial data are close to the constant equilibrium state in H2-framework. If the initial datas in Ll-norm are finite additionally, the optimal time decay rates of strong solutions are established. With the help of Fourier splitting method, one also establishes optimal time decay rates for the higher order spatial derivatives of director.

关键词： compressible nematic liquid crystal flows global solution Creen function long-time behavior

long-time evolution of charged grains in plasma under harmonic external force and after being withdrawn

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Chinese Physics B 2022年第2期31卷 460-464页

作者： Miao Guan Zhi-Dong Chen Meng-Die Li Zhong-Mao Liu You-Mei Wang Ming-Yang Yu Department of Physics School of ScienceHangzhou Dianzi UniversityHangzhou 310016China College of Engineering Physics CAMDTShenzhen Key Laboratory of Ultraintense Laser and Advanced Material TechnologyShenzhen Technology UniversityShenzhen 518118China Institute for Fusion Theory and Simulation Zhejiang UniversityHangzhou 310007China Theoretical Physics I Ruhr UniversityBochum D-44780Germany

Evolution of the charged grains in a two-dimensional dusty plasma under a spatially harmonic external force,in particular,their long-time behaviors after the force has been withdrawn,is studied by using molecular dynamics *** an external force and a grain–grain interaction force,initially homogeneously distributed grains can reach a quasistationary state in the form of a disk *** the external force is withdrawn,the disk moves initially with its size and shape nearly unchanged until it rapidly stops moving,and eventually the disk grain rotates like a *** time needed to reach the final state increases with the strength of the initial external force increasing.

关键词： dusty plasma external force long-time behavior molecular dynamics(MD)simulation

Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing

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Chinese Annals of Mathematics,Series B 2019年第6期40卷 967-1004页

作者： Gui-Qiang G.CHEN Peter H.C.PANG Mathematical Institute University of Oxford

Some recent developments in the analysis of long-time behaviors of stochastic solutions of nonlinear conservation laws driven by stochastic forcing are *** existence and uniqueness of invariant measures are established for anisotropic degenerate parabolic-hyperbolic conservation laws of second-order driven by white *** further developments,problems,and challenges in this direction are also discussed.

关键词： Stochastic solutions Entropy solutions Invariant measures Existence Uniqueness Stochastic forcing Anisotropic degenerate Parabolichyperbolic equations long-time behavior

Initial and Boundary Value Problem for a System of Balance Laws from Chemotaxis:Global Dynamics and Diffusivity Limit

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Annals of Applied Mathematics 2021年第1期37卷 61-110页

作者： Zefu Feng Jiao Xu Ling Xue Kun Zhao School of Mathematical Sciences Chongqing Normal UniversityChongqing 400047China SUSTech International Center for Mathematics Southern University of Science and TechnologyShenzhen 518055GuangdongChina College of Mathematical Sciences Harbin Engineering UniversityHarbin 150001HeilongjiangChina Department of Mathematics Tulane UniversityNew OrleansLA 70118USA

In this paper,we study long-time dynamics and diffusion limit of large-data solutions to a system of balance laws arising from a chemotaxis model with logarithmic sensitivity and nonlinear production/degradation *** energy methods,we show that under time-dependent Dirichlet boundary conditions,long-time dynamics of solutions are driven by their boundary data,and there is no restriction on the magnitude of initial ***,the zero chemical diffusivity limit is established under zero Dirichlet boundary conditions,which has not been observed in previous studies on related models.

关键词： Balance laws chemotaxis initial-boundary value problem dynamic boundary condition strong solution long-time behavior diffusivity limit