{
  "id": "1106.2116",
  "version": "v3",
  "published": "2011-06-10T16:48:30.000Z",
  "updated": "2011-09-19T09:16:12.000Z",
  "title": "Some new well-posedness results for the Klein-Gordon-Schrödinger system",
  "authors": [
    "Hartmut Pecher"
  ],
  "comment": "19 pages. Some typos corrected. Final version to be published in Differential and Integral Equations",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the Cauchy problem for the 2D and 3D Klein-Gordon-Schr\\\"odinger system. In 2D we show local well-posedness for Schr\\\"odinger data in H^s and wave data in H^{\\sigma} x H^{\\sigma -1} for s=-1/4 + and \\sigma = -1/2, whereas ill-posedness holds for s<- 1/4 or \\sigma <-1/2, and global well-posedness for s\\ge 0 and s- 1/2 \\le \\sigma < s+ 3/2. In 3D we show global well-posedness for s \\ge 0, s - 1/2 < \\sigma \\le s+1. Fundamental for our results are the studies by Bejenaru, Herr, Holmer and Tataru, and Bejenaru and Herr for the Zakharov system, and also the global well-posedness results for the Zakharov and Klein-Gordon-Schr\\\"odinger system by Colliander, Holmer and Tzirakis.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-09-19T09:16:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35L70"
    ],
    "keywords": [
      "klein-gordon-schrödinger system",
      "global well-posedness results",
      "ill-posedness holds",
      "cauchy problem",
      "local well-posedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 913798,
      "adsabs": "2011arXiv1106.2116P"
    }
  }
}