{
  "id": "math/0110049",
  "version": "v3",
  "published": "2001-10-04T00:06:58.000Z",
  "updated": "2006-07-14T00:54:39.000Z",
  "title": "Multilinear estimates for periodic KdV equations and applications",
  "authors": [
    "Jim Colliander",
    "Markus Keel",
    "Gigliola Staffilani",
    "Hideo Takaoka",
    "Terence Tao"
  ],
  "comment": "39 pages. A correction to the Case 3 argument in Section 14",
  "journal": "J. Funct. Anal. 211 (2004), 173-218",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove an endpoint multilinear estimate for the $X^{s,b}$ spaces associated to the periodic Airy equation. As a consequence we obtain sharp local well-posedness results for periodic generalized KdV equations, as well as some global well-posedness results below the energy norm. In particular we prove a multilinear estimate which completes the proof of global well-posedness for periodic KdV in a preceding paper (math.AP/0110045) down to the optimal regularity H^{-1/2}.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-07-14T00:54:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q53",
      "42B35",
      "37K10"
    ],
    "keywords": [
      "periodic kdv equations",
      "applications",
      "sharp local well-posedness results",
      "global well-posedness results",
      "endpoint multilinear estimate"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....10049C"
    }
  }
}