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

  • Martin Donati

    Université de Lyon, CNRS, Université Lyon 1, Institut Camille Jordan, 43 bd. du 11 novembre, Villeurbanne Cedex F-69622, France
  • Dragoș Iftimie

    Université de Lyon, CNRS, Université Lyon 1, Institut Camille Jordan, 43 bd. du 11 novembre, Villeurbanne Cedex F-69622, France
Long time confinement of vorticity around a stable stationary point vortex in a bounded planar domain cover

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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.

Cite this article

Martin Donati, Dragoș Iftimie, Long time confinement of vorticity around a stable stationary point vortex in a bounded planar domain. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 5, pp. 1461–1485

DOI 10.1016/J.ANIHPC.2020.11.009