不可压液晶模型经典解的存在性  

EXISTENCE OF CLASSICAL SOLUTIONS FOR THE INCOMPRESSIBLE LIQUID CRYSTAL MODEL

作　　者：陈嘉欢 江宁 CHEN Jia-huan;JIANG Ning(School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China)

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《数学杂志》2023年第1期1-21,共21页Journal of Mathematics

摘　　要：本文研究一个描述离子在向列型液晶中输运和扩散的非线性偏微分方程模型.该模型耦合了对应于电势满足Maxwell’s方程的离子的连续性方程的Nernst-Planck系统,控制液晶流演变的不可压Naiver-Stokes方程与关于液晶方向场的非线性Allen-Cahn型方程.我们利用能量方法证明了该系统的大初值经典解的局部存在性和小初值经典解的整体存在性.In this paper we study a system of nonlinear partial differential equations modelling the electrokinetics of a nematic electrolyte material consisting of various ions species contained in a nematic liquid crystal.[The system coupling a Nernst-Planck system for the ions concentrations with a Maxwell’s equation of electrostatics governing the evolution of the electrostatic potential,an incompressible Navier-Stokes equation for the velocity field and a non-smooth Allen-Cahn type equation for the nematic director field.] We use energy method to prove the local existence of classical solutions with large initial data and the global existence of classical solutions with small initial data.

关 键 词：液晶 能量方法 经典解 

分 类 号：O175.26[理学—数学]