Weak-strong uniqueness of hydrodynamic flow of nematic liquid crystals

This article concerns a simplified model for a hydrodynamic system of incompressible nematic liquid crystal materials. It is shown that the weak-strong uniqueness holds for the class of weak solutions provided that either $(mathbf{u}, ablamathbf{d})in C([0,T),L^3(mathbb{R}^3))$; or $(mathbf{u}, ablamathbf{d})in L^q(0,T; dot{B}^{-1+3/p+2/q}_{p,q} (mathbb{R}^3))$ with $2leq p1$.