  It is well known that the Euler vortex patch in $\mathbb{R}^{2}$ will remain
regular if it is regular enough initially. In bounded domains, the regularity
theory for patch solutions is less complete. In this paper, we study Euler
vortex patches in a general smooth bounded domain. We prove global in time
regularity by providing an upper bound on the growth of curvature of the patch
boundary. For a special symmetric scenario, we construct an example of double
exponential curvature growth, showing that our upper bound is qualitatively
sharp.
