An analytical and numerical study of steady patches in the disc

Francisco de la Hoz, Zineb Hassainia, Taoufik Hmidi, Joan Mateu

Research output: Contribution to journalArticlepeer-review

Abstract

We prove the existence of m-fold rotating patches for the Euler equations in the disc, for the simply connected and doubly connected cases. Compared to the planar case, the rigid boundary introduces rich dynamics for the lowest symmetries m = 1 and m = 2. We also discuss some numerical experiments highlighting the interaction between the boundary of the patch and the rigid one.

Original languageEnglish (US)
Pages (from-to)1609-1670
Number of pages62
JournalAnalysis and PDE
Volume9
Issue number7
DOIs
StatePublished - 2016

Keywords

  • Bifurcation
  • Euler equations
  • V-states

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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