3 papers
math.AP2026
Uniformly Rotating Euler Configurations with Multiple Vorticity Holes
Vittorio Baroncini, Juan Carlos Cantero, Claudia GarcÃa +3
We construct new families of uniformly rotating vortex-patch solutions of the two-dimensional incompressible Euler equations consisting of a simply connected outer patch and multip…
math.AP2026
The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations
Marc Magaña, Joan Mateu, Joan Orobitg
We prove the persistence of boundary smoothness of vortex patches for the quasi-geostrophic shallow-water (QGSW) equations. The QGSW equations generalize the Euler equations by inc…
math.AP2025
Explicit minimisers for anisotropic Riesz energies
Rupert L. Frank, Joan Mateu, Maria Giovanna Mora +3
In this paper we describe explicitly the energy minimisers of a class of nonlocal interaction energies where the attraction is quadratic, and the repulsion is Riesz-like and anisot…