{
  "id": "1311.5988",
  "version": "v1",
  "published": "2013-11-23T10:46:24.000Z",
  "updated": "2013-11-23T10:46:24.000Z",
  "title": "The Two Dimensional Euler Equations on Singular Exterior Domains",
  "authors": [
    "David Gérard-Varet",
    "Christophe Lacave"
  ],
  "categories": [
    "math.AP"
  ],
  "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 $L^p_{c}$ ($p>2$) 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).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-23T10:46:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dimensional euler equations",
      "singular exterior domains",
      "general initial vorticity",
      "global weak solutions",
      "singular domains"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00205-013-0617-9",
      "journal": "Archive for Rational Mechanics and Analysis",
      "year": 2013,
      "month": "Jul",
      "volume": 209,
      "number": 1,
      "pages": 131
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013ArRMA.209..131G"
    }
  }
}