Vortex patch problem for stratified euler equations

Taoufik Hmidi, Mohamed Zerguine

Research output: Contribution to journalArticlepeer-review

Abstract

We study in this paper the vortex patch problem for the stratified Euler equations in space dimension two. We generalize Chemin's result [J.Y. Chemin, Oxford University Press, 1998.] concerning the global persistence of the Ḧolderian regularity of the vortex patches. Roughly speaking, we prove that if the initial density is smooth and the initial vorticity takes the form ω0=1Ω, with Ω a C1+ε -bounded domain, then the velocity of the stratified Euler equations remains Lipschitz globally in time and the vorticity is split into two parts ω(t)=1Ωt+ρ{ogonek}(t), where Ωt denotes the image of Ω by the flow and has the same regularity of the domain Ω. The function ρ{ogonek} is a smooth function.

Original languageEnglish (US)
Pages (from-to)1541-1563
Number of pages23
JournalCommunications in Mathematical Sciences
Volume12
Issue number8
DOIs
StatePublished - 2014

Keywords

  • Para-differential calculus
  • Stratified system
  • Time decay
  • Vortex patches

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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