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Taoufik Hmidi; Joan Mateu
Corotating and counter-rotating vortex pairs for Euler equations
Journées équations aux dérivées partielles (2016), Exp. No. 6, 16 p., doi: 10.5802/jedp.647
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Class. Math.: 35Q35, 76B03, 76C05
Mots clés: Euler equations, steady vortex pairs, desingularization.

Résumé - Abstract

We study the existence of corotating and counter-rotating pairs of simply connected patches for Euler equations. From the numerical experiments implemented in [7, 16, 17] it is conjectured the existence of a curve of steady vortex pairs passing through the point vortex pairs. There are some analytical proofs based on variational principle [14, 18], however they do not give enough information about the pairs such as the uniqueness or the topological structure of each single vortex. We intend in this paper to give direct proofs confirming the numerical experiments. The proofs rely on the contour dynamics equations combined with a desingularization of the point vortex pairs and the application of the implicit function theorem.

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