{
  "id": "math/0307289",
  "version": "v2",
  "published": "2003-07-22T02:30:55.000Z",
  "updated": "2004-06-26T22:27:35.000Z",
  "title": "Global well-posedness of the Benjamin-Ono equation in H^1(R)",
  "authors": [
    "Terence Tao"
  ],
  "comment": "21 pages, no figures. Minor mathematical errors corrected",
  "journal": "J. Hyperbolic Differential Equations 1 (2004) 27-49",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that the Benjamin-Ono equation is globally well-posed in $H^s(\\R)$ for $s \\geq 1$. This is despite the presence of the derivative in the non-linearity, which causes the solution map to not be uniformly continuous in $H^s$ for any $s$. The main new ingredient is to perform a global gauge transformation which almost entirely eliminates this derivative.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-06-26T22:27:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q53"
    ],
    "keywords": [
      "benjamin-ono equation",
      "global well-posedness",
      "global gauge transformation",
      "solution map",
      "non-linearity"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......7289T"
    }
  }
}