Boundary Regularity of Rotating Vortex Patches

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Abstract

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. © 2013 Springer-Verlag Berlin Heidelberg.
Original languageEnglish
Pages (from-to)171-208
JournalArchive for Rational Mechanics and Analysis
Volume209
DOIs
Publication statusPublished - 1 Jul 2013

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