Weak solutions to the stationary incompressible Euler equations

2014/01/17 by Antoine Choffrut, László Székelyhidi, Choffrut, Antoine +1 · 3 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1401.4301

openalex publication_date 2014/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider weak stationary solutions to the incompressible Euler equations and show that the analogue of the h-principle obtained in [5, 7] for time-dependent weak solutions continues to hold. The key difference arises in dimension d = 2, where it turns out that the relaxation is strictly smaller than what one obtains in the time-dependent case.

Citations

• Transporting microstructure and dissipative Euler flows

Cited by

• Desingularization of nondegenerate rotating vortex patches
• Non-uniqueness of Admissible Weak Solutions to Compressible Euler Systems with Source Terms
• Remarks on radial symmetry of stationary and uniformly-rotating solutions for the 2D Euler equation

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