Steady vortex sheets in presence of surface tension

TL;DR

This paper proves a bifurcation result for steady vortex sheets with surface tension, analyzing how rotation speed, surface tension, or vorticity influence the existence of non-trivial solutions in a two-fluid model.

Contribution

It introduces a bifurcation analysis for vortex sheets considering surface tension effects, expanding understanding of steady configurations in fluid dynamics.

Findings

Existence of bifurcations near circular vortex sheets.

Dependence of bifurcation on rotation speed, surface tension, and vorticity.

Identification of conditions for non-trivial steady vortex sheets.

Abstract

We prove a bifurcation result of uniformly-rotating/stationary non-trivial vortex sheets near the circular distribution for a model of two irrotational fluids with same density taking into account surface tension effects. As bifurcation parameters, we play with either the speed of rotation, the surface tension coefficient or the mean vorticity.