The sharp corner formation in 2d Euler dynamics of patches: infinite double exponential rate of merging

TL;DR

This paper demonstrates that in 2D Euler patch dynamics with regular strain, the merging rate of patches can be accelerated to a double exponential rate over time, revealing extreme convergence behavior.

Contribution

It proves that the merging rate in 2D Euler patch dynamics with regular strain can be double exponential for all time, a novel result in fluid dynamics.

Findings

Merging rate can be double exponential in 2D Euler patches with regular strain.

Convergence to singular stationary solutions occurs at an extremely rapid rate.

The result advances understanding of singularity formation in fluid flows.

Abstract

For the 2d Euler dynamics of patches, we investigate the convergence to the singular stationary solutions in the presence of a regular strain. It is proved that the rate of merging can be made double exponential for all time.