Strong solutions for the Beris-Edwards model for nematic liquid crystals with homogeneous Dirichlet boundary conditions. (English) Zbl 1333.35174

Abels, Helmut; Dolzmann, Georg; Liu, Yuning

Adv. Differ. Equ. 21, No. 1-2, 109-152 (2016).

Summary: 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.

MSC:

35Q35	PDEs in connection with fluid mechanics
35Q30	Navier-Stokes equations
76D03	Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05	Navier-Stokes equations for incompressible viscous fluids
76A15	Liquid crystals

Keywords:

strong solutions; Beris-Edwards model; nematic liquid crystals; Navier-Stokes equations