Article Dans Une Revue Indiana University Mathematics Journal Année : 2023

Co-rotating vortices with N fold symmetry for the inviscid surface quasi-geostrophic equation

Résumé

We provide a variational construction of special solutions to the generalized surface quasi-geostrophic equations. These solutions take the form of N vortex patches with N-fold symmetry , which are steady in a uniformly rotating frame. Moreover, we investigate their asymptotic properties when the size of the corresponding patches vanishes. In this limit, we prove these solutions to be a desingularization of N Dirac masses with the same intensity, located on the N vertices of a regular polygon rotating at a constant angular velocity.

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hal-02967850 , version 1 (15-10-2020)

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Ludovic Godard-Cadillac, Philippe Gravejat, Didier Smets. Co-rotating vortices with N fold symmetry for the inviscid surface quasi-geostrophic equation. Indiana University Mathematics Journal, 2023, 72 (2), pp.603-650. ⟨10.1512/iumj.2023.72.9206⟩. ⟨hal-02967850⟩
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