  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.
