Uniqueness for the 2-D Euler equations on domains with corners

2013/07/02 by Christophe Lacave, Lacave, Christophe, Évelyne Miot +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1307.0622

openalex publication_date 2013/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a large class of non smooth bounded domains, existence of a global weak solution of the 2D Euler equations, with bounded vorticity, was established by Gérard-Varet and Lacave. In the case of sharp domains, the question of uniqueness for such weak solutions is more involved due to the bad behavior of Δ^-1 close to the boundary. In the present work, we show uniqueness for any bounded and simply connected domain with a finite number of corners of angles smaller than π/2. Our strategy relies on a log-Lipschitz type regularity for the velocity field.

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