The Two Dimensional Euler Equations on Singular Exterior Domains

Abstract

This paper is a follow-up of article [Gerard-Varet and Lacave, ARMA 2013], on the existence of global weak solutions to the two dimensional Euler equations in singular domains. In [Gerard-Varet and Lacave, ARMA 2013], we have established the existence of weak solutions for a large class of bounded domains, with initial vorticity in $L^p$ ($p>1$). For unbounded domains, we have proved a similar result only when the initial vorticity is in $L_c^p$ ($p>2$) and when the domain is the exterior of a single obstacle. The goal here is to retrieve these two restrictions: we consider general initial vorticity in $L^1\cap L^p$ ($p>1$), outside an arbitrary number of obstacles (not reduced to points).

References in corpus (5)

• The Euler Equations in planar nonsmooth convex domains
• Grisvard's shift theorem near L^infinity and Yudovich theory on polygonal domains
• Uniqueness for two dimensional incompressible ideal flow on singular domains
• Uniqueness for the 2-D Euler equations on domains with corners
• Permeability through a perforated domain for the incompressible 2D Euler equations

Cited by in corpus (4)

• Topography influence on the Lake equations in bounded domains
• The Euler Equations in Planar Domains with Corners
• Uniqueness for the 2-D Euler equations on domains with corners
• Euler Equations on General Planar Domains