Stability in $L^1$ of circular vortex patches

TL;DR

This paper proves that circular vortex patches in ideal, incompressible fluids are stable in the $L^1$ norm, regardless of initial perturbation size, within a broad class of bounded patches.

Contribution

It establishes the $L^1$ stability of circular vortex patches without size restrictions, extending previous results to a more general setting.

Findings

Circular vortex patches are stable in $L^1$ norm.

Stability holds for all bounded patches of equal strength.

No restrictions on initial perturbation size.

Abstract

The motion of incompressible and ideal fluids is studied in the plane. The stability in $L^1$ of circular vortex patches is established among the class of all bounded vortex patches of equal strength without any restriction on the size of the initial perturbation.