Regularity and uniqueness for a class of solutions to the hydrodynamic flow of nematic liquid crystals
Abstract
In this paper, we establish an $\epsilon$-regularity criterion for any weak solution $(u,d)$ to the nematic liquid crystal flow (1.1) such that $(u,\nabla d)\in L^p_tL^q_x$ for some $p\ge 2$ and $q\ge n$ satisfying the condition (1.2). As consequences, we prove the interior smoothness of any such a solution when $p>2$ and $q>n$. We also show that uniqueness holds for the class of weak solutions $(u,d)$ the Cauchy problem of the nematic liquid crystal flow (1.1) that satisfy $(u,\nabla d)\in L^p_tL^q_x$ for some $p>2$ and $q>n$ satisfying (1.2).
- Publication:
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arXiv e-prints
- Pub Date:
- May 2014
- DOI:
- 10.48550/arXiv.1405.6737
- arXiv:
- arXiv:1405.6737
- Bibcode:
- 2014arXiv1405.6737H
- Keywords:
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- Mathematics - Analysis of PDEs