Boundary Regularity of Rotating Vortex Patches

Juan Eugenio Mateu Bennassar; Taoufik Hmidi; Joan Verdera

doi:https://doi.org/10.1007/s00205-013-0618-8

Boundary Regularity of Rotating Vortex Patches

Juan Eugenio Mateu Bennassar, Taoufik Hmidi, Joan Verdera

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

29 Citations (Scopus)

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 language	English
Pages (from-to)	171-208
Journal	Archive for Rational Mechanics and Analysis
Volume	209
DOIs	https://doi.org/10.1007/s00205-013-0618-8
Publication status	Published - 1 Jul 2013

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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. {\textcopyright} 2013 Springer-Verlag Berlin Heidelberg.",

author = "{Mateu Bennassar}, {Juan Eugenio} and Taoufik Hmidi and Joan Verdera",

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AU - Mateu Bennassar, Juan Eugenio

AU - Hmidi, Taoufik

AU - Verdera, Joan

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Y1 - 2013/7/1

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. © 2013 Springer-Verlag Berlin Heidelberg.

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. © 2013 Springer-Verlag Berlin Heidelberg.

U2 - https://doi.org/10.1007/s00205-013-0618-8

DO - https://doi.org/10.1007/s00205-013-0618-8

M3 - Article

VL - 209

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EP - 208

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

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