Electron. J. Diff. Equ., Vol. 2012 (2012), No. 182, pp. 1-16.

Weak-strong uniqueness of hydrodynamic flow of nematic liquid crystals

Ji-hong Zhao, Qiao Liu

Abstract:
This article concerns a simplified model for a hydrodynamic system of incompressible nematic liquid crystal materials. It is shown that the weak-strong uniqueness holds for the class of weak solutions provided that either $(\hbox{\bf u}, \nabla\hbox{\bf d})\in C([0,T),L^3(\mathbb{R}^3))$; or $(\hbox{\bf u}, \nabla\hbox{\bf d})\in L^q(0,T; \dot{B}^{-1+3/p+2/q}_{p,q} (\mathbb{R}^3))$ with $2\leq p<\infty$, $2<q<\infty$ and $\frac{3}{p}+\frac{2}{q}>1$.

Submitted July 12, 2012. Published October 19, 2012.
Math Subject Classifications: 35A02, 35B35, 76A15.
Key Words: Nematic liquid crystal flow; weak solutions; stability; weak-strong uniqueness.

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Ji-hong Zhao
College of Science, Northwest A&F University
Yangling, Shaanxi 712100, China
email: zhaojihong2007@yahoo.com.cn
Qiao Liu
Department of Mathematics, Hunan Normal University
Changsha, Hunan 410081, China
email: liuqao2005@163.com

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