  We consider a 2D system that models the nematic liquid crystal flow through
the Navier--Stokes equations suitably coupled with a
transport-reaction-diffusion equation for the averaged molecular orientations.
This system has been proposed as a reasonable approximation of the well-known
Ericksen--Leslie system. Taking advantage of previous well-posedness results
and proving suitable dissipative estimates, here we show that the system
endowed with periodic boundary conditions is a dissipative dynamical system
with a smooth global attractor of finite fractal dimension.
