A Uniqueness theorem for the Vortex-Wave system with non-constant vorticity near the point vortex
Year: 2026
Type: preprint
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 $|w_0(x)-w_0(X_0)|=O(|x-X_0|^α)$ for $α> 2$ and the vorticity is in $L^\infty$, then solutions are unique, globally in time, even though the velocity is not log-Lipschitz.
Source: arXiv (Cornell University)
Author: Meyer, David
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204951433