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

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
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