Uniqueness of Positive Vorticity Solutions to the 2D Euler Equations on Singular Domains

2022/06/03 by Zonglin Han, Han, Zonglin, Andrej Zlatoš +1
Earth and Planetary Sciences · Engineering · Mathematics · #Aeolian processes and effects #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2206.01405

openalex publication_date 2022/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that particle trajectories for positive vorticity solutions to the 2D Euler equations on fairly general bounded simply connected domains cannot reach the boundary in finite time. This includes domains with possibly nowhere C¹ boundaries and having corners with arbitrary angles, and can fail without the sign hypothesis when the domain has large angle corners. Hence positive vorticity solutions on such domains are Lagrangian, and we also obtain their uniqueness if the vorticity is initially constant near the boundary.

Related

• Euler Equations on General Planar Domains
• Uniqueness for the 2-D Euler equations on domains with corners
• Uniqueness of the 2D Euler equation on rough domains
• Uniqueness of the 2D Euler equation on a corner domain with non-constant vorticity around the corner
• Wellposedness and singularity formation beyond the Yudovich class