Work

Vorticity blowup in 2D compressible Euler equations

Year: 2026

Type: article

Abstract: We prove finite-time vorticity blowup for smooth solutions of the 2D compressible Euler equations with smooth, localized, and nonvacuous 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 codimension stability.

Source: Duke Mathematical Journal

DOI: 10.1215/00127094-2025-0061

Authors: Jiajie Chen, Giorgio Cialdea, Steve Shkoller, Vlad Vicol

Institutions: University of Chicago, Courant Institute of Mathematical Sciences, New York University, University of California, Davis

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Shock formation and interface motion in fluids, Singularity Formation in Fluid Mechanics and Related Equations, Collaborative Research: Shock formation, shock development, and the propagation of singularities in fluid dynamics, Collaborative Research: Shock formation, shock development, and the propagation of singularities in fluid dynamics