{
  "id": "1305.0773",
  "version": "v1",
  "published": "2013-05-03T16:52:04.000Z",
  "updated": "2013-05-03T16:52:04.000Z",
  "title": "Non-uniqueness for the Euler equations: the effect of the boundary",
  "authors": [
    "Claude Bardos",
    "László Székelyhidi Jr.",
    "Emil Wiedemann"
  ],
  "comment": "20 pages. Dedicated to the memory of Professor Mark Vishik",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP",
    "physics.flu-dyn"
  ],
  "abstract": "We consider rotational initial data for the two-dimensional incompressible Euler equations on an annulus. Using the convex integration framework, we show that there exist infinitely many admissible weak solutions (i.e. such with non-increasing energy) for such initial data. As a consequence, on bounded domains there exist admissible weak solutions which are not dissipative in the sense of P.-L. Lions, as opposed to the case without physical boundaries. Moreover we show that admissible solutions are dissipative provided they are H\\\"{o}lder continuous near the boundary of the domain.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-03T16:52:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q31",
      "76B03",
      "35D30",
      "76F40"
    ],
    "keywords": [
      "admissible weak solutions",
      "non-uniqueness",
      "convex integration framework",
      "rotational initial data",
      "two-dimensional incompressible euler equations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1070/RM2014v069n02ABEH004886",
      "journal": "Russian Mathematical Surveys",
      "year": 2014,
      "month": "Apr",
      "volume": 69,
      "number": 2,
      "pages": 189
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014RuMaS..69..189B"
    }
  }
}