Strong solutions to the density-dependent incompressible nematic liquid crystal flows

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Gao, Jincheng¹  Tao, Qiang²  Yao, Zheng-an¹ 

[1] Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China

[2] Shenzhen Univ, Sch Math & Stat, Shenzhen 518060, Peoples R China

关键词: Incompressible nematic liquid crystal flows;    Density-dependent;    Strong solutions;    Blowup criterion;   

DOI  :  10.1016/j.jde.2015.10.047

来源: Elsevier

【 摘 要 】

In this paper, we investigate the density-dependent incompressible nematic liquid crystal flows in n-dimensional (n = 2 or 3) bounded domain. The local existence and uniqueness of strong solutions are obtained when the viscosity coefficient of fluid depends on density. Furthermore, one establishes blowup criterions for the regularity of the strong solutions in dimensions two and three respectively. In particular, we build a blowup criterion just in terms of the gradient of density if the initial direction field satisfies some geometric configuration. For these results, the initial density need not be strictly positive. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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