WILD SOLUTIONS OF THE 3D AXISYMMETRIC EULER EQUATIONS

Brkic P, Wiedemann E (2025)

Publication Type: Journal article

Publication year: 2025

Journal

SIAM Journal on Mathematical Analysis Society for Industrial and Applied Mathematics

Book Volume: 57

Pages Range: 996-1020

Journal Issue: 1

DOI: 10.1137/24M1653914

Abstract

We consider the Cauchy problem for the 3D incompressible axisymmetric swirl-free Euler equations. The convex integration method developed by De Lellis and Székelyhidi rules out the possibility that the Euler equations admit unique admissible weak solutions. It had remained conceivable, though, that axisymmetry of the solution might serve as a selection criterion. Using a surprising link to 2D isentropic compressible Euler equations, we will show that this is not the case: There exists initial data for which there are infinitely many admissible swirl-free axisymmetric weak solutions of the 3D incompressible Euler equations. Moreover, somewhat conversely, we show that there exists an axisymmetric swirl-free initial velocity for which the axisymmetry breaks down instantaneously.

Authors with CRIS profile

Emil Wiedemann Lehrstuhl für Analysis

Involved external institutions

Universität Ulm DE Germany (DE)

How to cite

APA:

Brkic, P., & Wiedemann, E. (2025). WILD SOLUTIONS OF THE 3D AXISYMMETRIC EULER EQUATIONS. SIAM Journal on Mathematical Analysis, 57(1), 996-1020. https://doi.org/10.1137/24M1653914

MLA:

Brkic, Patrick, and Emil Wiedemann. "WILD SOLUTIONS OF THE 3D AXISYMMETRIC EULER EQUATIONS." SIAM Journal on Mathematical Analysis 57.1 (2025): 996-1020.

BibTeX: Download