Existence of steady multiple vortex patches to the vortex-wave system

TL;DR

This paper proves the existence of steady multiple vortex patch solutions in a bounded domain for the vortex-wave system, using variational methods and asymptotic analysis as vorticity strength increases.

Contribution

It introduces a novel variational approach to establish steady multiple vortex patches in bounded domains for the vortex-wave system.

Findings

Existence of steady multiple vortex patches proven.

Construction via variational problem for vorticity.

Asymptotic behavior analyzed as vorticity strength tends to infinity.

Abstract

In this paper we prove the existence of steady multiple vortex patch solutions to the vortex-wave system in a planar bounded domain. The construction is performed by solving a certain variational problem for the vorticity and studying its asymptotic behavior as the vorticity strength goes to infinity.