  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.
