Vorticity blowup in 2D compressible Euler equations

TL;DR

This paper proves that smooth solutions to the 2D compressible Euler equations can develop finite-time vorticity blowup, with stable axisymmetric implosion and swirl velocity, marking a significant advance in understanding singularity formation.

Contribution

It establishes the occurrence of finite-time vorticity blowup in 2D compressible Euler equations with stable swirl velocity, a novel result in fluid dynamics.

Findings

Finite-time vorticity blowup proven for smooth solutions.

Vorticity blowup coincides with the first singularity.

Stable axisymmetric implosion observed with full swirl velocity stability.

Abstract

We prove finite-time vorticity blowup for smooth solutions of the 2D compressible Euler equations with smooth, localized, and non-vacuous initial data. The vorticity blowup occurs at the time of the first singularity, and is accompanied by an axisymmetric implosion in which the swirl velocity enjoys full stability, as opposed to finite co-dimension stability.