Archive for Rational Mechanics and Analysis

, Volume 209, Issue 1, pp 171–208 | Cite as

Boundary Regularity of Rotating Vortex Patches

  • Taoufik Hmidi
  • Joan Mateu
  • Joan Verdera


We show that the boundary of a rotating vortex patch (or V-state, in the terminology of Deem and Zabusky) is C , provided the patch is close to the bifurcation circle in the Lipschitz norm. The rotating patch is also convex if it is close to the bifurcation circle in the C 2 norm. Our proof is based on Burbea’s approach to V-states.


Vorticity Unit Disc Conformal Mapping Jordan Curve Open Unit Disc 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.IRMARUniversité de Rennes 1Rennes CedexFrance
  2. 2.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterra, BarcelonaSpain

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