Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 182, pp. 1-16.
Title: Weak-strong uniqueness of hydrodynamic flow of
nematic liquid crystals
Authors: Ji-hong Zhao (Northwest A&F Univ., Yangling, Shaanxi, China)
Qiao Liu (Hunan Normal Univ., Changsha, Hunan, China)
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
$(\mathbf{u}, \nabla\mathbf{d})\in C([0,T),L^3(\mathbb{R}^3))$; or
$(\mathbf{u}, \nabla\mathbf{d})\in L^q(0,T; \dot{B}^{-1+3/p+2/q}_{p,q}
(\mathbb{R}^3))$ with
$2\leq p<\infty$, $21$.
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.