  In this article we study the regularity of the topological and metric entropy
of partially hyperbolic flows with two-dimensional center direction. We show
that the topological entropy is upper semicontinuous with respect to the flow,
and we give an example where the lower semicontinuity fails. We also show that
if such a flow has no fixed points, then it is entropy expansive, and
consequently the metric entropy function is upper semicontinuous, there exist
equilibrium states (and measures of maximal entropy), and principal symbolic
extensions.
