  We consider the Beris-Edwards model describing nematic liquid crystal
dynamics and restrict to a shear flow and spatially homogeneous situation. We
analyze the dynamics focusing on the effect of the flow. We show that in the
co-rotational case one has gradient dynamics, up to a periodic eigenframe
rotation, while in the non-co-rotational case we identify the short and long
time regime of the dynamics. We express these in terms of the physical
variables and compare with the predictions of other models of liquid crystal
dynamics.
