Publications [#341002] of Alexander A. Kiselev

Papers Published

1. Kiselev, A; Li, C, Global regularity and fast small-scale formation for Euler patch equation in a smooth domain, Communications in Partial Differential Equations, vol. 44 no. 4 (April, 2019), pp. 279-308 [doi]
   (last updated on 2024/04/24)

   Abstract:
   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.