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arXiv · 2107.12820

On the dynamics of point vortices for the 2D Euler equation with $L^p$ vorticity

Stefano Ceci·Christian Seis
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Abstract

We study the evolution of solutions to the 2D 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 $L^p$ 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.

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Stefano Ceci, Christian Seis. 2021-07-27. On the dynamics of point vortices for the 2D Euler equation with $L^p$ vorticity. https://doi.org/10.1098/rsta.2021.0046

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