{
  "id": "1701.08678",
  "version": "v1",
  "published": "2017-01-30T16:22:12.000Z",
  "updated": "2017-01-30T16:22:12.000Z",
  "title": "Onsager's conjecture for admissible weak solutions",
  "authors": [
    "Tristan Buckmaster",
    "Camillo De Lellis",
    "László Székelyhidi Jr.",
    "Vlad Vicol"
  ],
  "comment": "36 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove that given any $\\beta<1/3$, a time interval $[0,T]$, and given any smooth energy profile $e \\colon [0,T] \\to (0,\\infty)$, there exists a weak solution $v$ of the three-dimensional Euler equations such that $v \\in C^{\\beta}([0,T]\\times \\mathbb{T}^3)$, with $e(t) = \\int_{\\mathbb{T}^3} |v(x,t)|^2 dx$ for all $t\\in [0,T]$. Moreover, we show that a suitable $h$-principle holds in the regularity class $C^\\beta_{t,x}$, for any $\\beta<1/3$. The implication of this is that the dissipative solutions we construct are in a sense typical in the appropriate space of subsolutions as opposed to just isolated examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-30T16:22:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q31",
      "35D30",
      "76B03"
    ],
    "keywords": [
      "admissible weak solutions",
      "onsagers conjecture",
      "three-dimensional euler equations",
      "time interval",
      "principle holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}