On rotating doubly connected vortices

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© 2014 Elsevier Inc. In this paper we consider rotating doubly connected vortex patches for the Euler equations in the plane. When the inner interface is an ellipse we show that the exterior interface must be a confocal ellipse. We then discuss some relations, first found by Flierl and Polvani, between the parameters of the ellipses, the velocity of rotation and the magnitude of the vorticity in the domain enclosed by the inner ellipse.
Original languageEnglish
Pages (from-to)1395-1429
JournalJournal of Differential Equations
Publication statusPublished - 1 Jan 2015


  • 2D incompressible Euler equations
  • Inverse problems
  • Potential theory
  • Rotating patches


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