{
  "id": "1711.00321",
  "version": "v1",
  "published": "2017-11-01T12:54:35.000Z",
  "updated": "2017-11-01T12:54:35.000Z",
  "title": "Geometric Hydrodynamics via Madelung Transform",
  "authors": [
    "Boris Khesin",
    "Gerard Misiolek",
    "Klas Modin"
  ],
  "comment": "17 pages, 2 figures",
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We introduce a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that several important PDEs of hydrodynamical origin can be described in this framework in a natural way. In particular, the Madelung transform between the Schr\\\"odinger equation and Newton's equations is a symplectomorphism of the corresponding phase spaces. Furthermore, the Madelung transform turns out to be a K\\\"ahler map when the space of densities is equipped with the Fisher-Rao information metric. We describe several dynamical applications of these results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-01T12:54:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric hydrodynamics",
      "madelung transform turns",
      "study newtons equations",
      "smooth probability densities",
      "fisher-rao information metric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}