On the evolution of a concentrated vortex in an ideal fluid (Q1091868)

The paper contains an analysis of the asymptotic nature of the point vortex idealization/approximation. The results are restricted to a single point vortex \((N=1)\) in a bounded simply-connected domain in the plane. It is proved that as the initial vorticity tends to a delta measure located at some initial point, the corresponding solutions of the Euler equations tend in the distributional sense to the point vortex described by the Kirchhoff-Routh equations, and the convergence is valid over an arbitrary time. This establishes the ''desingularization'' of the Kirchhoff-Routh equations by vortex flows with asymptotically concentrated vorticity. The corresponding results for several vortices (N\(\geq 2)\), however, remains still open.