Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (6): 1671-1683.

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Serrin's Type Solutions of the Incompressible Liquid Crystals System

Jianzhong Min1,*,Xiangao Liu2(),Zixuan Liu2()   

  1. 1 Science and Arts Faculty, Shanghai University of Medicine and Health Sciences, Shanghai 201318
    2 School of Mathematical Sciences, Fudan University, Shanghai 200433
  • Received:2020-10-23 Online:2021-12-26 Published:2021-12-02
  • Contact: Jianzhong Min;
  • Supported by:
    Supported by the NSFC(11631011);Supported by the NSFC(11971113)


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