{
  "id": "1702.04327",
  "version": "v1",
  "published": "2017-02-14T18:29:25.000Z",
  "updated": "2017-02-14T18:29:25.000Z",
  "title": "The Biot-Savart operator of a bounded domain",
  "authors": [
    "Alberto Enciso",
    "Maria de los Angeles Garcia-Ferrero",
    "Daniel Peralta-Salas"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We construct the analog of the Biot-Savart integral for bounded domains. Specifically, we show that the velocity field of an incompressible fluid with tangency boundary conditions on a bounded domain can be written in terms of its vorticity using an integral kernel $K_\\Omega(x,y)$ that has an inverse-square singularity on the diagonal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-14T18:29:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded domain",
      "biot-savart operator",
      "tangency boundary conditions",
      "inverse-square singularity",
      "biot-savart integral"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}