We consider a generalization of the standard Beris-Edwards system
modeling incompressible liquid crystal flows of nematic type. This
couples a Navier-Stokes system for the fluid velocity with an evolution
equation for the Q-tensors variable describing the direction of liquid
crystal molecules. The convergence at infinite time for global solutions
is studied and we prove that whole trajectory goes to a single
equilibrium by using a Lojasiewicz-Simon's result.