Euler evolution of a concentrated vortex in planar bounded domains

الأصل · EN

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 ε, then the time evolved vorticity is also supported in a small region with diameter d, d≤ Cεα for any α<1/3, and the center of the vorticity tends to the point vortex, the motion of which is described by the Kirchhoff-Routh equation.