{
  "id": "math/0702079",
  "version": "v3",
  "published": "2007-02-05T14:50:29.000Z",
  "updated": "2007-11-27T10:37:55.000Z",
  "title": "The Euler equations as a differential inclusion",
  "authors": [
    "Camillo De Lellis",
    "László Székelyhidi Jr"
  ],
  "comment": "16 pages; v2: corrected typos, simplified some proofs; v3: 20 pages, added a second (more direct) proof",
  "journal": "Ann. of Math. (2) 170 (2009), no. 3, 1417-1436",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we propose a new point of view on weak solutions of the Euler equations, describing the motion of an ideal incompressible fluid in $\\mathbb{R}^n$ with $n\\geq 2$. We give a reformulation of the Euler equations as a differential inclusion, and in this way we obtain transparent proofs of several celebrated results of V. Scheffer and A. Shnirelman concerning the non-uniqueness of weak solutions and the existence of energy--decreasing solutions. Our results are stronger because they work in any dimension and yield bounded velocity and pressure.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-11-27T10:37:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76B03",
      "35D05",
      "76F99"
    ],
    "keywords": [
      "euler equations",
      "differential inclusion",
      "weak solutions",
      "ideal incompressible fluid",
      "transparent proofs"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2079D"
    }
  }
}