A uniqueness and regularity criterion for Q-tensor models with Neumann boundary conditions

Abstract

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 (∂tu, ∂tQ). 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.