Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 173, pp. 1-5.

Title: Regularity of solutions to 3-D nematic liquid crystal flows

Authors: Qiao Liu     (Sun Yat-sen Univ., Guangzhou, China)
         Shangbin Cui (Sun Yat-sen Univ., Guangzhou, China)

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 06, 2010.
Math Subject Classifications: 76A15, 35B65, 35Q35.
Key Words: Liquid crystal flow; initial value problem;
           regularity of solutions.