Euler evolution of a concentrated vortex in planar bounded domains
Abstract
In this paper, we consider the time evolution of an ideal fluid in a planar bounded domain. We prove that if the initial vorticity is supported in a sufficiently small region with diameter , then the time evolved vorticity is also supported in a small region with diameter d, d≤ Cα for any α<13, and the center of the vorticity tends to the point vortex, the motion of which is described by the Kirchhoff-Routh equation.
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