{
  "id": "1301.3586",
  "version": "v1",
  "published": "2013-01-16T05:03:01.000Z",
  "updated": "2013-01-16T05:03:01.000Z",
  "title": "Exact solutions to the Navier-Stokes equation for an incompressible flow from the interpretation of the Schroedinger wave function",
  "authors": [
    "Vladimir V. Kulish",
    "Jose L. Lage"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP",
    "physics.flu-dyn"
  ],
  "abstract": "The existence of the velocity potential is a direct consequence from the derivation of the continuity equation from the Schroedinger equation. This implies that the Cole-Hopf transformation is applicable to the Navier-Stokes equation for an incompressible flow and allows reducing the Navier-Stokes equation to the Einstein-Kolmogorov equation, in which the reaction term depends on the pressure. The solution to the resulting equation, and to the Navier-Stokes equation as well, can then be written in terms of the Green's function of the heat equation and is given in the form of an integral mapping. Such a form of the solution makes bifurcation period doubling possible, i.e. solutions to transition and turbulent flow regimes in spite of the existence of the velocity potential.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-16T05:03:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30"
    ],
    "keywords": [
      "navier-stokes equation",
      "schroedinger wave function",
      "incompressible flow",
      "exact solutions",
      "velocity potential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}