{
  "id": "math/0607039",
  "version": "v2",
  "published": "2006-07-03T08:55:44.000Z",
  "updated": "2007-04-13T22:53:50.000Z",
  "title": "Global Existence and Uniqueness of Solutions to the Maxwell-Schr{ö}dinger Equations",
  "authors": [
    "Makoto Nakamura",
    "Takeshi Wada"
  ],
  "comment": "30 pages. In the revised version, the following modification was made. (1) A line for dedication was added in the first page. (2) Some lines were added at the bottom in page 4 and the top in page 5 in the first section to make the description accurate. (3) Some typographical errors were corrected throughout the paper",
  "doi": "10.1007/s00220-007-0337-9",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The time local and global well-posedness for the Maxwell-Schr{\\\"o}dinger equations is considered in Sobolev spaces in three spatial dimensions. The Strichartz estimates of Koch and Tzvetkov type are used for obtaining the solutions in the Sobolev spaces of low regularities. One of the main results is that the solutions exist time globally for large data.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-04-13T22:53:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q40",
      "35Q55",
      "35L70"
    ],
    "keywords": [
      "dinger equations",
      "global existence",
      "uniqueness",
      "maxwell-schr",
      "sobolev spaces"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Commun. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}