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 [Formula: see text] integrable for some [Formula: see text], 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)'.

Keywords: Euler equations; stability estimates; vortex dynamics.