## Advances in Differential Equations

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

#### Abstract

Existence and uniqueness of local strong solutions 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 $\Omega\subset\mathbb{R}^d$ 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.

#### Article information

Source
Adv. Differential Equations, Volume 21, Number 1/2 (2016), 109-152.

Dates
First available in Project Euclid: 23 November 2015

Permanent link to this document
https://projecteuclid.org/euclid.ade/1448323166

Mathematical Reviews number (MathSciNet)
MR3449332

Zentralblatt MATH identifier
1333.35174

#### Citation

Abels, Helmut; Dolzmann, Georg; Liu, YuNing. Strong solutions for the Beris-Edwards model for nematic liquid crystals with homogeneous Dirichlet boundary conditions. Adv. Differential Equations 21 (2016), no. 1/2, 109--152. https://projecteuclid.org/euclid.ade/1448323166