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arXiv · 2010.07361

Vortex patches choreography for active scalar equations

C. García
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Abstract

This paper deals with the existence of $N$ vortex patches located at the vertex of a regular polygon with $N$ sides that rotate around the center of the polygon at a constant angular velocity. That is done for Euler and (SQG)$_\beta$ equations, with $\beta\in(0,1)$, but may be also extended to more general models. The idea is the desingularization of the Thomsom polygon for the $N$ point vortex system, that is, $N$ point vortices located at the vertex of a regular polygon with $N$ sides. The proof is based on the study of the contour dynamics equation combined with the application of the infinite dimensional Implicit Function theorem and the well--chosen of the function spaces.

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C. García. 2020-10-14. Vortex patches choreography for active scalar equations. https://doi.org/10.1007/s00332-021-09729-x

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