2020/10/16 by Godard-Cadillac, Ludovic, Gravejat, Philippe, Smets, Didier · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2010.08194
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.