Boundary Regularity of Rotating Vortex Patches

Taoufik Hmidi; Joan Mateu; Joan Verdera

doi:10.1007/s00205-013-0618-8

Boundary Regularity of Rotating Vortex Patches

Taoufik Hmidi, Joan Mateu, Joan Verdera

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	171-208
Number of pages	38
Journal	Archive for Rational Mechanics and Analysis
Volume	209
Issue number	1
DOIs	https://doi.org/10.1007/s00205-013-0618-8
State	Published - Jul 2013

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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title = "Boundary Regularity of Rotating Vortex Patches",

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.",

author = "Taoufik Hmidi and Joan Mateu and Joan Verdera",

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AU - Verdera, Joan

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N2 - 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.

AB - 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.

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Boundary Regularity of Rotating Vortex Patches

Abstract

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