Global regularity and fast small-scale formation for Euler patch equation in a smooth domain


Journal Article

© 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.

Full Text

Duke Authors

Cited Authors

  • Kiselev, A; Li, C

Published Date

  • April 3, 2019

Published In

Volume / Issue

  • 44 / 4

Start / End Page

  • 279 - 308

Electronic International Standard Serial Number (EISSN)

  • 1532-4133

International Standard Serial Number (ISSN)

  • 0360-5302

Digital Object Identifier (DOI)

  • 10.1080/03605302.2018.1546318

Citation Source

  • Scopus