  We study a Q-tensor problem modeling the dynamic of nematic liquid crystals
in 3D domains. The system consists of the Navier-Stokes equations, with an
extra stress tensor depending on the elastic forces of the liquid crystal,
coupled with an Allen-Cahn system for the Q-tensor variable. This problem has a
dissipative in time free-energy which leads, in particular, to prove the
existence of global in time weak solutions. We analyze the large-time behavior
of the weak solutions. By using a Lojasiewicz-Simon's result, we prove the
convergence as time goes to infinity of the whole trajectory to a single
equilibrium.
