Finite time blow-up for the nematic liquid crystal flow in dimension two

Chen-Chih Lai, Fanghua Lin, Changyou Wang, Juncheng Wei, Yifu Zhou

Published 2019-08-28Version 1

We consider the initial-boundary value problem of a simplified nematic liquid crystal flow in a bounded, smooth domain $\Omega \subset \mathbb R^2$. Given any $k$ distinct points in the domain, we develop a new {\em inner--outer gluing method} to construct solutions which blow up exactly at those $k$ points as $t$ goes to a finite time $T$. Moreover, we obtain a precise description of the blow-up.