不可压液晶方程组的Serrin解

Abstract

Abstract:

In this paper, we study the nematic liquid crystals system under the simplified Ginzburg-Landau model, which is probably the simplest mathematical model that one can derive, without destroying the basic nonlinear structure [1]. We get the local existence and uniquness of the Serrin's type of solutions provided the initial data $u_{0}\in L^{p}\cap H, $ $d_{0}\in W^{1, p}, p\geq n$. According to the Serrin's regularity criteria for the incompressible liquid crystals system [2], we actually prove the local existence of smooth solutions to liquid crystals system for big data and global existence of smooth solutions for small data.

Key words: Existence, Liquid crystal, Serrin's criterion, Uniqueness

CLC Number:

O175

Jianzhong Min,Xiangao Liu,Zixuan Liu. Serrin's Type Solutions of the Incompressible Liquid Crystals System[J].Acta mathematica scientia,Series A, 2021, 41(6): 1671-1683.

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References 16

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Serrin's Type Solutions of the Incompressible Liquid Crystals System

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