From point vortices to vortex patches in self-similar expanding configurations

Abstract

The main result is that given a generic self-similarly expanding configuration of 3 point vortices that start sufficiently far out, we can instead take compactly supported vorticity functions, and the resulting solution to 2D incompressible Euler will evolve like a nearby point vortex configuration for all time, with the size of the patches growing at most as $t^{1/4+\epsilon}$ and the distance between them growing as $\sqrt{t}$.