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arXiv · 1908.10955

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

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

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.

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Chen-Chih Lai, Fanghua Lin, Changyou Wang, Juncheng Wei, Yifu Zhou. 2019-08-28. Finite time blow-up for the nematic liquid crystal flow in dimension two. https://arxiv.org/abs/1908.10955

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