{
  "id": "1011.0591",
  "version": "v1",
  "published": "2010-11-02T12:10:54.000Z",
  "updated": "2010-11-02T12:10:54.000Z",
  "title": "Strichartz estimates for partially periodic solutions to Schrödinger equations in 4d and applications",
  "authors": [
    "Sebastian Herr",
    "Daniel Tataru",
    "Nikolay Tzvetkov"
  ],
  "comment": "15 pages",
  "journal": "J. Reine Angew. Math. (2012), Vol. 2014, No. 690, 65-78",
  "doi": "10.1515/crelle-2012-0013",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the energy critical nonlinear Schr\\\"odinger equation on periodic domains of the form R^m x T^{4-m} with m=0,1,2,3. Assuming that a certain L^4 Strichartz estimate holds for solutions to the corresponding linear Schr\\\"odinger equation, we prove that the nonlinear problem is locally well-posed in the energy space. Then we verify that the L^4 estimate holds if m=2,3, leaving open the cases m=0,1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-02T12:10:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55"
    ],
    "keywords": [
      "partially periodic solutions",
      "schrödinger equations",
      "applications",
      "strichartz estimate holds",
      "periodic domains"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.0591H"
    }
  }
}