三维液晶方程一个与水平速度相关的改进正则性准则

A Refined Regularity Criterion for $3$D Liquid Crystal Equations Involving Horizontal Velocity

中文关键词:  液晶流  正则性准则  局部强解

英文关键词:liquid crystal flow  regularity criterion  local strong solution

中文摘要:

      根据速度的水平分量$u_h$的垂直导数,本文研究了3维液晶方程的整体正则性,具体地,当速度的水平分量$u_h$的垂直导数满足$\partial_3u_h\in L^p(0,T; R^3), \frac{2}{p}+\frac{3}{q}\le \frac{3}{2}$, $2\le p\le \infty$,则局部强解$(u,d)$可以光滑的延拓出$t=T$.

英文摘要:

      This note investigates the global regularity of $3$D liquid crystal equations in terms of the vertical derivative of $u_h$. More precisely, we prove that if the vertical derivative of the horizontal velocity component $u_h$ satisfies $\pa_3u_h\in L^p(0,T; \R^3)$ with $\frac{2}{p}+\frac{3}{q}\le \frac{3}{2}$, $2\le p\le \infty$, then the local strong solution $(u,d)$ can be smoothly extended beyond $t=T$.