A Uniqueness theorem for the Vortex-Wave system with non-constant vorticity near the point vortex
David Meyer
Abstract
We study the uniqueness of the vortex wave system, i.e.\ the 2D incompressible Euler equations with vorticity consisting of a point vortex and a bounded part. We show that if the initial vorticity and point vortex location (w0,X0) satisfy a constraint of the type |w0(x)-w0(X0)|=O(|x-X0|α) for α> 2 and the vorticity is in L∞, then solutions are unique, globally in time, even though the velocity is not log-Lipschitz.
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