{
  "id": "0910.4653",
  "version": "v1",
  "published": "2009-10-25T12:35:22.000Z",
  "updated": "2009-10-25T12:35:22.000Z",
  "title": "The Cauchy Problem of the Schrödinger-Korteweg-de Vries System",
  "authors": [
    "Yifei Wu"
  ],
  "comment": "38 pages,1 figure",
  "journal": "Differential and Integral Equations, 23 (2010), 569-600",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the Cauchy problem of the Schr\\\"odinger-Korteweg-de Vries system. First, we establish the local well-posedness results, which improve the results of Corcho, Linares (2007). Moreover, we obtain some ill-posedness results, which show that they are sharp in some well-posedness thresholds. Particularly, we obtain the local well-posedness for the initial data in $H^{-{3/16}+}(\\R)\\times H^{-{3/4}+}(\\R)$ in the resonant case, it is almost the optimal except the endpoint. At last we establish the global well-posedness results in $H^s(\\R)\\times H^s(\\R)$ when $s>\\dfrac{1}{2}$ no matter in the resonant case or in the non-resonant case, which improve the results of Pecher (2005).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-25T12:35:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q53",
      "35Q55"
    ],
    "keywords": [
      "schrödinger-korteweg-de vries system",
      "cauchy problem",
      "local well-posedness results",
      "global well-posedness results",
      "ill-posedness results"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.4653W"
    }
  }
}