Regularity of solutions to 3-D nematic liquid crystal flows

• Main Authors: Qiao Liu, Shangbin Cui
• Format: Article
• Language: English
• Published: Texas State University 2010-12-01
• Series: Electronic Journal of Differential Equations
• Subjects: Liquid crystal flow; initial value problem; regularity of solutions
• Online Access: http://ejde.math.txstate.edu/Volumes/2010/173/abstr.html

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