Boundary Regularity of Rotating Vortex Patches
By Taoufik Hmidi, Joan Mateu, Joan Verdera. 2012
126 citations recorded by the source corpus.
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 C2 norm. Our proof is based on Burbea’s approach to V-states.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7ef668de998331b6a43b8c5ecf8cf9a59a80603d
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In Applied Mathematics
- A. Castro
- D. C'ordoba
- Javier G'omez-Serrano
- Joan Mateu
- Taoufik Hmidi
- Peter Constantin
- Thomas Alazard
- Vlad Vicol
In Mathematical Physics
- D. C'ordoba
- A. Castro
- Javier G'omez-Serrano
- Taoufik Hmidi
- Dong Li
- Vlad Vicol
- Peter Constantin
- José L. Rodrigo
Citations in the corpus
- Degenerate bifurcation of the rotating patches (2015, background): “Recently, Verdera and the authors studied in [17] the regularity of the V-states close to the disc and proved that the boundaries are in fact of class C∞ and convex.”
- Existence and regularity of rotating global solutions for the generalized surface quasi-geostrophic equations (2014, methodology): “These solutions are also known to exist for the vortex patch problem (α = 0), see the paper [18] by Hmidi, Mateu and Verdera, and recently their existence has been shown for the case 0 < α < 1 [16] by Hassainia and Hmidi.”