Weak compactness of simplified nematic liquid flows in 2D

Abstract

For any bounded, smooth domain $\Omega \subset {\mathbb{R}}^2$, %(or $\Omega ={\mathbb{R}}^2$), we will establish the weak compactness property of solutions to the simplified Ericksen-Leslie system for both uniaxial and biaxial nematics, and the convergence of weak solutions of the Ginzburg-Landau type nematic liquid crystal flow to a weak solution of the simplified Ericksen-Leslie system as the parameter tends to zero. This is based on the compensated compactness property of the Ericksen stress tensors, which is obtained by the $L^p$-estimate of the Hopf differential for the Ericksen-Leslie system and the Pohozaev type argument for the Ginzburg-Landau type nematic liquid crystal flow.

16 pages

References in corpus (1)

• On static and hydrodynamic biaxial nematic liquid crystals

Cited by in corpus (2)

• From the Landau-de Gennes theory to the Ericksen-Leslie theory in dimension two
• Global weak solutions to the Stochastic Ericksen--Leslie equations in dimension two