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

TL;DR

This paper proves the existence and uniqueness of local strong solutions for a modified Beris-Edwards model describing nematic liquid crystals, incorporating variable viscosity and boundary conditions, using linearization and fixed-point methods.

Contribution

It establishes the first local strong solution results for the Beris-Edwards model with variable viscosity and homogeneous Dirichlet boundary conditions.

Findings

Existence of local strong solutions is proven.

Uniqueness of solutions is established.

The model includes viscosity dependence on the Q-tensor.

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.