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

On the long-time behavior of some mathematical models for nematic liquid crystals