Global Bifurcation of Rotating Vortex Patches

Zineb Hassainia, Nader Masmoudi, Miles H. Wheeler

Research output: Contribution to journalArticlepeer-review


We rigorously construct continuous curves of rotating vortex patch solutions to the two-dimensional Euler equations. The curves are large in that, as the parameter tends to infinity, the minimum along the interface of the angular fluid velocity in the rotating frame becomes arbitrarily small. This is consistent with the conjectured existence [30, 38] of singular limiting patches with 90 corners at which the relative fluid velocity vanishes. For solutions close to the disk, we prove that there are “cat's-eyes”-type structures in the flow, and provide numerical evidence that these structures persist along the entire solution curves and are related to the formation of corners. We also show, for any rotating vortex patch, that the boundary is analytic as soon as it is sufficiently regular.

Original languageEnglish (US)
Pages (from-to)1933-1980
Number of pages48
JournalCommunications on Pure and Applied Mathematics
Issue number9
StatePublished - Sep 1 2020

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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