A UNIQUENESS AND REGULARITY CRITERION FOR Q-TENSOR MODELS WITH NEUMANN BOUNDARY CONDITIONS

We give a regularity criterion for a Q-tensor system modeling a nematic Liquid Crystal, under homogeneous Neumann boundary conditions for the tensor Q. Starting of a criterion only imposed on the velocity field u two results are proved; the uniqueness of weak solutions and the global in time weak regularity for the time derivative (partial derivative(t)u,partial derivative(t)Q). This paper extends the work done in [8] for a nematic Liquid Crystal model formulated in (u, d), where d denotes the orientation vector of the liquid crystal molecules.