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  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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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. 1461–1485DOI 10.1016/J.ANIHPC.2020.11.009