English

Long time confinement of vorticity around a stable stationary point vortex in a bounded planar domain

Analysis of PDEs 2020-12-24 v1

Abstract

In this paper we consider the incompressible Euler equation in a simply-connected bounded planar domain. We study the confinement of the vorticity around a stationary point vortex. We show that the power law confinement around the center of the unit disk obtained in [2] remains true in the case of a stationary point vortex in a simply-connected bounded domain. The domain and the stationary point vortex must satisfy a condition expressed in terms of the conformal mapping from the domain to the unit disk. Explicit examples are discussed at the end.

Keywords

Cite

@article{arxiv.2012.12574,
  title  = {Long time confinement of vorticity around a stable stationary point vortex in a bounded planar domain},
  author = {Martin Donati and Dragos Iftimie},
  journal= {arXiv preprint arXiv:2012.12574},
  year   = {2020}
}

Comments

Will appear in Annales de l'Institut Henri Poincar\'e C, Analyse Non Lin\'eaire