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A Uniqueness theorem for the Vortex-Wave system with non-constant vorticity near the point vortex
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 (w0,X0) satisfy a constraint of the type |w0(x)−w0(X0)|=O(|x−X0|α) for α> 2 and the vorticity is in L∞, then solutions are unique, globally in time, even though the velocity is not log-Lipschitz.
Related
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BibTeX
@misc{meyer2026uniqueness,
title = {{A Uniqueness theorem for the Vortex-Wave system with non-constant vorticity near the point vortex}},
author = {David Meyer},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29721},
eprint = {2608.29721},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29721},
}
RIS
TY - UNPB
TI - A Uniqueness theorem for the Vortex-Wave system with non-constant vorticity near the point vortex
AU - David Meyer
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29721
UR - https://arxiv.org/abs/2608.29721
AB - 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^∞, then solutions are unique, globally in time, even though the velocity is not log-Lipschitz.
ER -