Strong solutions for the Beris-Edwards model for nematic liquid crystals with homogeneous Dirichlet boundary conditions

2013/12/20 by Abels, Helmut, Dolzmann, Georg, Liu, YuNing · 1 citation
#35Q30 #35Q35 #76D03 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1312.5988

Abstract

Existence and uniqueness of local strong solution for the Beris--Edwards model for nematic liquid crystals, which couples the Navier-Stokes equations with an evolution equation for the Q-tensor, is established on a bounded domain in the case of homogeneous Dirichlet boundary conditions. The classical Beris--Edwards model is enriched by including a dependence of the fluid viscosity on the Q-tensor. The proof is based on a linearization of the system and Banach's fixed-point theorem.

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• The global well-posedness for the Q-tensor model of nematic liquid crystals in the half-space

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