  A model describing the evolution of a liquid crystal substance in the nematic
phase is investigated in terms of two basic state variables: the {\it velocity
field} $\bu$ and the {\it director field} $\di$, representing the preferred
orientation of molecules in a neighborhood of any point in a reference domain.
After recalling a known existence result, we investigate the long-time behavior
of weak solutions. In particular, we show that any solution trajectory admits a
non-empty $\omega$-limit set containing only stationary solutions. Moreover, we
give a number of sufficient conditions in order that the $\omega$-limit set
contains a single point. Our approach improves and generalizes existing results
on the same problem.
