Global regularity and fast small-scale formation for Euler patch equation in a smooth domain
© 2019, © 2019 Taylor & Francis Group, LLC. It is well known that the Euler vortex patch in 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 article, 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.
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