  We consider the vortex patch problem for both the 2-D and 3-D incompressible
Euler equations. In 2-D, we prove that for vortex patches with $H^{k-0.5}$
Sobolev-class contour regularity, $k \ge 4$, the velocity field on both sides
of the vortex patch boundary has $H^k$ regularity for all time. In 3-D, we
establish existence of solutions to the vortex patch problem on a finite-time
interval $[0,T]$, and we simultaneously establish the $H^{k-0.5}$ regularity of
the two-dimensional vortex patch boundary, as well as the $H^k$ regularity of
the velocity fields on both sides of vortex patch boundary, for $k \ge 3$.
