On the stability of a singular vortex dynamics

TL;DR

This paper investigates the stability of singular vortex dynamics, specifically the persistence of corners in vortex structures under small perturbations, using advanced mathematical transforms and scattering theory.

Contribution

It introduces a novel analysis of vortex corner stability employing the Hasimoto transform and scattering theory for a variable-coefficient Gross-Pitaevski equation.

Findings

Corners in vortex dynamics remain stable under small regular perturbations.

The Hasimoto transform effectively analyzes vortex singularities.

Long-range scattering properties are crucial for understanding vortex stability.

Abstract

In this paper we address the question of the singular vortex dynamics exhibited in [15], which generates a corner in finite time. The purpose is to prove that under some appropriate small regular perturbation the corner still remains. Our approach uses the Hasimoto transform and deals with the long range scattering properties of a Gross-Pitaevski equation with time-variable coefficients.