Well-Posedness of a Fully Coupled Navier--Stokes/Q-tensor System with Inhomogeneous Boundary Data

摘要: We prove short-time well-posedness and existence of global weak solutions the Beris--Edwards model for nematic liquid crystals in case a bounded domain with inhomogeneous mixed Dirichlet Neumann boundary conditions. The system consists Navier--Stokes equations coupled an evolution equation $Q$-tensor. possess higher regularity time order one compared to class finite energy. This is enough obtain Lipschitz continuity nonlinear terms corresponding function spaces. Therefore shown aid contraction mapping principle using that linearized isomorphism between associated