Bifurcation of rotating patches from Kirchhoff vortices

TL;DR

This paper proves the existence of multiple rotating patch solutions bifurcating from elliptical shapes at specific angular velocities, advancing understanding of vortex dynamics.

Contribution

It establishes the existence of countable bifurcation branches of rotating patches from Kirchhoff vortices, a novel result in vortex theory.

Findings

Countable bifurcation branches from elliptical vortices.

Existence of rotating patches at specific angular velocities.

Mathematical proof of bifurcation phenomena.

Abstract

In this paper we prove the existence of countable branches of rotating patches bifurcating from the ellipses at some implicit angular velocities.