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 $\epsilon$, then the time evolved vorticity is also supported in a small region with diameter $d$, $d\le C{\epsilon }^{\alpha }$ for any $\alpha <\frac{1}{3}$, and the center of the vorticity tends to the point vortex, the motion of which is described by the Kirchhoff-Routh equation.

arXiv comment15 pages