{
  "id": "1401.2655",
  "version": "v1",
  "published": "2014-01-12T18:20:59.000Z",
  "updated": "2014-01-12T18:20:59.000Z",
  "title": "Serfati solutions to the 2D Euler equations on exterior domains",
  "authors": [
    "David M. Ambrose",
    "James P. Kelliher",
    "Milton C. Lopes Filho",
    "Helena J. Nussenzveig Lopes"
  ],
  "comment": "50 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove existence and uniqueness of a weak solution to the incompressible 2D Euler equations in the exterior of a bounded smooth obstacle when the initial data is a bounded divergence-free velocity field having bounded scalar curl. This work completes and extends the ideas outlined by P. Serfati for the same problem in the whole-plane case. With non-decaying vorticity, the Biot-Savart integral does not converge, and thus velocity cannot be reconstructed from vorticity in a straightforward way. The key to circumventing this difficulty is the use of the Serfati identity, which is based on the Biot-Savart integral, but holds in more general settings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-12T18:20:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q31",
      "76B03"
    ],
    "keywords": [
      "exterior domains",
      "serfati solutions",
      "biot-savart integral",
      "bounded divergence-free velocity field",
      "incompressible 2d euler equations"
    ],
    "publication": {
      "doi": "10.1016/j.jde.2015.06.001",
      "journal": "Journal of Differential Equations",
      "year": 2015,
      "month": "Nov",
      "volume": 259,
      "number": 9,
      "pages": 4509
    },
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JDE...259.4509A"
    }
  }
}