  We consider a model case for a strictly convex domain of dimension $d\geq 2$
with smooth boundary and we describe dispersion for the wave equation with
Dirichlet boundary conditions. More specifically, we obtain the optimal fixed
time decay rate for the smoothed out Green function: a $t^{1/4}$ loss occurs
with respect to the boundary less case, due to repeated occurrences of
swallowtail type singularities in the wave front set.
