On the rate of merging of vorticity level sets for the 2D Euler equations

TL;DR

This paper demonstrates that in the 2D Euler equations on a disc, two different vorticity level sets can approach each other exponentially fast along a curve, revealing rapid mixing behavior.

Contribution

It establishes the possibility of arbitrarily fast merging of vorticity level sets in 2D Euler flows, a novel insight into the dynamics of vorticity.

Findings

Vorticity level sets can approach each other exponentially fast.

The result applies to solutions on a disc.

It highlights rapid mixing phenomena in 2D Euler flows.

Abstract

We show that two distinct level sets of the vorticity of a solution to the 2D Euler equations on a disc can approach each other along a curve at an arbitrarily large exponential rate.