On the estimate of distance traveled by a particle in a disk-like vortex patch

Abstract

We consider the incompressible two-dimensional Euler equation in the plane in the case when its initial vorticity is the characteristic function of a bounded open set. We show that the travel distance grows linearly for most of fluid particles initially placed on the set when the area of the symmetric difference between the set and a disk is small enough.

arXiv comment6 pages