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. 2022 Jun 27;380(2226):20210046.
doi: 10.1098/rsta.2021.0046. Epub 2022 May 9.

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

Stefano Ceci  1 , Christian Seis  1
Affiliations

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

Stefano Ceci et al. Philos Trans A Math Phys Eng Sci. .

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.

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