Existence of small loops in a bifurcation diagram near degenerate eigenvalues

Taoufik Hmidi, Coralie Renault

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study the global structure of a bifurcation diagram for rotating doubly connected patches near a degenerate case for incompressible Euler equations. We show that branches with the same symmetry merge, forming a small loop, provided that they are close enough. This gives an analytical proof for the numerical observations conducted in the recent work by de la Hoz et al (2016 SIAM J. Math. Anal. 48 1892-928).

Original languageEnglish (US)
Pages (from-to)3821-3852
Number of pages32
JournalNonlinearity
Volume30
Issue number10
DOIs
StatePublished - Sep 15 2017

Keywords

  • bifurcation diagram
  • Euler equations
  • relative equilibria

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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