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Existence and uniqueness of local strong solution for the Beris--Edwardsmodel for nematic liquid crystals, which couples the Navier-Stokes equationswith an evolution equation for the Q-tensor, is established on a bounded domainin the case of homogeneous Dirichlet boundary conditions. The classicalBeris--Edwards model is enriched by including a dependence of the fluidviscosity on the Q-tensor. The proof is based on a linearization of the systemand Banach's fixed-point theorem.

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