Bifurcation of rotating patches from kirchhoff vortices

Taoufik Hmidi, Joan Mateu

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we investigate the existence of a new family of rotating patches for the planar Euler equations. We shall prove the existence of countable branches bifurcating from the ellipses at some implicit angular velocities. The proof uses bifurcation tools combined with the explicit parametrization of the ellipse through the exterior conformal mappings. The boundary is shown to belong to Hölderian class.

Original languageEnglish (US)
Pages (from-to)5401-5422
Number of pages22
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume36
Issue number10
DOIs
StatePublished - Oct 2016

Keywords

  • Bifurcation
  • Kirchhoff vortices
  • Rotating patches

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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