On the dynamics of point vortices for the two-dimensional Euler equation with Lp vorticity

Abstract

We study the evolution of solutions to the two-dimensional Euler equations whose vorticity is sharply concentrated in the Wasserstein sense around a finite number of points. Under the assumption that the vorticity is merely Lp integrable for some p>2, we show that the evolving vortex regions remain concentrated around points, and these points are close to solutions to the Helmholtz–Kirchhoff point vortex system. This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’.