Electron. J. Diff. Equ., Vol. 2010(2010), No. 173, pp. 1-5.

Regularity of solutions to 3-D nematic liquid crystal flows

Qiao Liu, Shangbin Cui

Abstract:
In this note we consider the regularity of solutions to 3-D nematic liquid crystal flows, we prove that if either $u\in L^{q}(0,T;L^p(\mathbb{R}^3))$, $\frac{2}{q}+\frac{3}{p}\leq1$, $3<p\leq\infty$; or $u\in L^{\alpha}(0,T;L^{\beta}(\mathbb{R}^3))$, $\frac{2}{\alpha}+\frac{3}{\beta}\leq 2$, $\frac{3}{2}< \beta\leq\infty$, then the solution $(u,d)$ is regular on $(0,T]$.

Submitted November 4, 2010. Published December 6, 2010.
Math Subject Classifications: 76A15, 35B65, 35Q35.
Key Words: Liquid crystal flow; initial value problem; regularity of solutions.

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Qiao Liu
Department of Mathematics, Sun Yat-sen University
Guangzhou, Guangdong 510275, China
email: liuqao2005@lzu.cn, liuqao2005@163.com
  Shangbin Cui
Department of Mathematics, Sun Yat-sen University
Guangzhou, Guangdong 510275, China
email: cuisb3@yahoo.com.cn

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