A Uniqueness theorem for the Vortex-Wave system with non-constant vorticity near the point vortex

David Meyer

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arXiv · 2608.29721

A Uniqueness theorem for the Vortex-Wave system with non-constant vorticity near the point vortex

David Meyer

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Abstract

We study the uniqueness of the vortex wave system, i.e.\ the 2D incompressible Euler equations with vorticity consisting of a point vortex and a bounded part. We show that if the initial vorticity and point vortex location $(w_0,X_0)$ satisfy a constraint of the type $|w_0(x)-w_0(X_0)|=O(|x-X_0|^\alpha)$ for $\alpha> 2$ and the vorticity is in $L^\infty$, then solutions are unique, globally in time, even though the velocity is not log-Lipschitz.

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David Meyer. 2026-08-30. A Uniqueness theorem for the Vortex-Wave system with non-constant vorticity near the point vortex. https://arxiv.org/abs/2608.29721

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