Strong solutions of the compressible nematic liquid crystal flow

被引：124

作者：

Huang, Tao ^{[1
]}

Wang, Changyou ^{[1
]}

Wen, Huanyao ^{[2
]}

机构：

[1] Univ Kentucky, Dept Math, Lexington, KY 40506 USA

[2] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2012年 / 252卷 / 03期

基金：

美国国家科学基金会;

关键词：

Compressible fluid; Nematic liquid crystal flow; Strong solutions; Blow-up criterions; EXISTENCE; EQUATIONS;

D O I：

10.1016/j.jde.2011.07.036

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study strong solutions of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in a domain Omega subset of R-3. We first prove the local existence of a unique strong solution provided that the initial data rho(0), u(0), d(0) are sufficiently regular and satisfy a natural compatibility condition. The initial density function rho(0) may vanish on an open subset (i.e., an initial vacuum may exist). We then prove a criterion for possible breakdown of such a local strong solution at finite time in terms of blow up of the quantities parallel to rho parallel to(Lt infinity Lx infinity) and parallel to del d parallel to(Lt3Lx infinity) (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：2222 / 2265

页数：44

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