In this paper, we consider a complex fluid modeling nematic liquid crystal
flows, which is described by a system coupling Navier-Stokes equations with a
parabolic Q-tensor system. We first prove the global existence of weak
solutions in dimension three. Furthermore, the global well-posedness of strong
solutions is studied with sufficiently large viscosity of fluid. Finally, we
show a continuous dependence result on the initial data which directly yields
the weak-strong uniqueness of solutions