{
  "id": "0704.3110",
  "version": "v1",
  "published": "2007-04-24T03:19:07.000Z",
  "updated": "2007-04-24T03:19:07.000Z",
  "title": "On the blowing up of solutions to quantum hydrodynamic models on bounded domains",
  "authors": [
    "Irene M. Gamba",
    "Maria Pia Gualdani",
    "Ping Zhang"
  ],
  "comment": "14 pages",
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "The blow-up in finite time for the solutions to the initial-boundary value problem associated to the multi-dimensional quantum hydrodynamic model in a bounded domain is proved. The model consists on conservation of mass equation and a momentum balance equation equivalent to a compressible Euler equations corrected by a dispersion term of the third order in the momentum balance. The proof is based on a-priori estimates for the energy functional for a new observable constructed with an auxiliary function, and it is shown that, under suitable boundary conditions and assumptions on the initial data, the solution blows up after a finite time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-04-24T03:19:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded domain",
      "multi-dimensional quantum hydrodynamic model",
      "finite time",
      "momentum balance equation equivalent",
      "solution blows"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.3110G"
    }
  }
}