Two-Point Vortex Confinement in a simply connected domain
Mathematical Physics
2025-12-08 v1 Classical Analysis and ODEs
math.MP
Abstract
This paper investigates the vortex confinement property of the two-point vortex system in a planar domain. We compute the time over which initial point vortices around a stable stationary point remain within a slightly larger ball. In particular, we show that this concentration persists indefinitely regardless of the vorticity strengths. In the borderline of the stability condition, we show that this time becomes a power law, if in addition, one relaxes the size of the stability ball.
Keywords
Cite
@article{arxiv.2512.05574,
title = {Two-Point Vortex Confinement in a simply connected domain},
author = {Slim Ibrahim and Ruixun Qin and Shengyi Shen},
journal= {arXiv preprint arXiv:2512.05574},
year = {2025}
}
Comments
Accepted by Discrete and Continuous Dynamical Systems on Nov. 27, 2025