Boundary Regularity of Rotating Vortex Patches |
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| Authors: | Taoufik Hmidi Joan Mateu Joan Verdera |
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| Institution: | 1. IRMAR, Université de Rennes 1, Campus de Beaulieu, 35 042, Rennes Cedex, France
2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Catalonia, Spain
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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. |
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