Trajectories of a single point vortex in a domain with two stable points and an unstable one.

Trajectories of a single point vortex in a domain with two stable points and an unstable one.

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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 bou...

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Context 1
... one of the eigenvalues is negative, then x 0 is said to be unstable, because there exists a point vortex evolving on a level set going away from x 0 . This notion of stability is the same as the one introduced in [15], Chapter 3. Figure 1 shows examples of the two situations. ...