Long time confinement of multiple concentrated vortices

TL;DR

This paper investigates the stability of multiple concentrated vortices in 2D Euler flows, demonstrating they remain separated and concentrated over extended time scales, with new energy stability estimates.

Contribution

It introduces a novel stability analysis for multiple vortices, extending the known time scales for their concentration and separation in fluid dynamics.

Findings

Vortices remain concentrated and separated over longer time scales.

A new stability estimate for the logarithmic interaction energy is established.

The results extend previous understanding of vortex stability in 2D Euler equations.

Abstract

We study the stability of multiple almost circular concentrated vortices in a fluid evolving according to the two-dimensional Euler equations. We show that, for general configurations, they must remain concentrated on time-scales much longer than previously known as long as they remain separated. We further prove a new stability estimate for the logarithmic interaction energy as part of the proof.