Global solution to the nematic liquid crystal flows with heat effect

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Bian, Dongfen^1,2  Xiao, Yao³ 

[1] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

[2] Beijing Inst Technol, Beijing Key Lab MCAACI, Beijing 100081, Peoples R China

[3] Chinese Univ Hong Kong, IMS, Room 614,Acad Bldg 1, Shatin, Hong Kong, Peoples R China

关键词: Nematic liquid crystal;    Strong solution;    Local solution;    Strong solution;    Maximal regularity;    Heat effect;   

DOI  :  10.1016/j.jde.2017.06.019

来源: Elsevier

【 摘 要 】

The temperature-dependent incompressible nematic liquid crystal flows in a bounded domain Omega subset of R-N (N = 2, 3) are studied in this paper. Following Danchin's method in [7], we use a localization argument to recover the maximal regularity of Stokes equation with variable viscosity, by which we first prove the local existence of a unique strong solution, then extend it to a global one provided that the initial data is a sufficiently small perturbation around the trivial equilibrium state. This paper also generalizes Hu-Wang's result in [21] to the non-isothermal case. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free