{
  "id": "0909.0793",
  "version": "v2",
  "published": "2009-09-04T01:23:11.000Z",
  "updated": "2009-10-08T04:20:53.000Z",
  "title": "Weak Continuity of the Flow Map for the Benjamin-Ono Equation on the Line",
  "authors": [
    "Shangbin Cui",
    "Carlos E. Kenig"
  ],
  "comment": "34 pages, no figures. This new version modifies the previous one in accordance with the referee's comments",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we show that the floow map of the Benjamin-Ono equation on the line is weakly continuous in L2(R), using \"local smoothing\" estimates. L2(R) is believed to be a borderline space for the local well-posedness theory of this equation. In the periodic case, Molinet [27] has recently proved that the flow map of the Benjamin-Ono equation is not weakly continuous in L2(T). Our results are in line with previous work on the cubic nonlinear Schrodinger equation, where Goubet and Molinet [11] showed weak continuity in L2(R) and Molinet [28] showed lack of weak continuity in L2(T).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-10-08T04:20:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L70"
    ],
    "keywords": [
      "benjamin-ono equation",
      "flow map",
      "cubic nonlinear schrodinger equation",
      "local well-posedness theory",
      "periodic case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.0793C"
    }
  }
}