Long time confinement of vorticity around a stable stationary point vortex in a bounded planar domain
Donati, Martin1 ; Iftimie, Dragoș1
1 Université de Lyon, CNRS, Université Lyon 1, Institut Camille Jordan, 43 bd. du 11 novembre, Villeurbanne Cedex F-69622, France
Annales de l'I.H.P. Analyse non linéaire, septembre – octobre 2021, Tome 38 (2021) no. 5, pp. 1461-1485.
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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.

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DOI : 10.1016/j.anihpc.2020.11.009
Mots-clés : Perfect incompressible flows, Point-vortex system, Confinement of vorticity
Donati, Martin 1 ; Iftimie, Dragoș 1

1 Université de Lyon, CNRS, Université Lyon 1, Institut Camille Jordan, 43 bd. du 11 novembre, Villeurbanne Cedex F-69622, France 
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Donati, Martin; Iftimie, Dragoș. Long time confinement of vorticity around a stable stationary point vortex in a bounded planar domain. Annales de l'I.H.P. Analyse non linéaire, septembre – octobre 2021, Tome 38 (2021) no. 5, pp. 1461-1485. doi : 10.1016/j.anihpc.2020.11.009. http://www.numdam.org/articles/10.1016/j.anihpc.2020.11.009/

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