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 ${{\textbf{u}}}$ two results are proved; the uniqueness of weak solutions and the global in time weak regularity for the time derivative $(\partial_t {{\textbf{u}}},\partial_t Q)$. This paper extends the work done in [8] for a nematic Liquid Crystal model formulated in $({{\textbf {u}}},{{\textbf {d}}})$, where ${{\textbf {d}}}$ denotes the orientation vector of the liquid crystal molecules.