{
  "id": "0904.1129",
  "version": "v1",
  "published": "2009-04-07T12:29:22.000Z",
  "updated": "2009-04-07T12:29:22.000Z",
  "title": "Counterexamples to Strichartz estimates for the magnetic Schroedinger equation",
  "authors": [
    "Luca Fanelli",
    "Andoni Garcia"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In space dimension $n\\geq3$, we consider the magnetic Schr\\\"odinger Hamiltonian $H=-(\\nabla-iA(x))^2$ and the corresponding Schr\\\"odinger equation i\\partial_tu+Hu=0. We show some explicit examples of potentials $A$, with less than Coulomb decay, for which any solution of this equation cannot satisfy Strichartz estimates, in the whole range of Schr\\\"odinger admissibility.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-07T12:29:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L05",
      "58J45"
    ],
    "keywords": [
      "magnetic schroedinger equation",
      "counterexamples",
      "satisfy strichartz estimates",
      "space dimension",
      "explicit examples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.1129F"
    }
  }
}