{
  "id": "0810.3445",
  "version": "v3",
  "published": "2008-10-20T00:36:21.000Z",
  "updated": "2009-04-20T02:06:04.000Z",
  "title": "Global Well-posedness of Korteweg-de Vries equation in $H^{-3/4}(\\R)$",
  "authors": [
    "Zihua Guo"
  ],
  "comment": "20 pages, 0 figure",
  "journal": "J. Math. Pures Appl. 91 (2009) 583-597",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove that the Korteweg-de Vries initial-value problem is globally well-posed in $H^{-3/4}(\\R)$ and the modified Korteweg-de Vries initial-value problem is globally well-posed in $H^{1/4}(\\R)$. The new ingredient is that we use directly the contraction principle to prove local well-posedness for KdV equation at $s=-3/4$ by constructing some special resolution spaces in order to avoid some 'logarithmic divergence' from the high-high interactions. Our local solution has almost the same properties as those for $H^s (s>-3/4)$ solution which enable us to apply the I-method to extend it to a global solution.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-04-20T02:06:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q53"
    ],
    "keywords": [
      "korteweg-de vries equation",
      "global well-posedness",
      "modified korteweg-de vries initial-value problem",
      "special resolution spaces",
      "local solution"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.3445G"
    }
  }
}