Full well-posedness of point vortex dynamics corresponding to stochastic 2D Euler equations

Abstract

The motion of a finite number of point vortices on a two-dimensional periodic domain is considered. In the deterministic case it is known to be well posed only for almost every initial configuration. Coalescence of vortices may occur for certain initial conditions. We prove that when a generic stochastic perturbation compatible with the Eulerian description is introduced, the point vortex motion becomes well posed for every initial configuration, in particular coalescence disappears.