Global regularity and fast small scale formation for Euler patch equation in a disk
arXiv:1703.09674
Abstract
It is well known that the Euler vortex patch in will remain regular if it is regular enough initially. In bounded domains, the regularity theory for patch solutions is less complete. We study here the Euler vortex patch in a disk. We prove global in time regularity by providing the upper bound of the growth of curvature of the patch boundary. For a special symmetric scenario, we construct an example of double exponential curvature growth, showing that such upper bound is qualitatively sharp.