{
  "id": "1004.3133",
  "version": "v2",
  "published": "2010-04-19T09:15:44.000Z",
  "updated": "2010-09-15T14:53:02.000Z",
  "title": "A note on ill-posedness for the KdV equation",
  "authors": [
    "Luc Molinet"
  ],
  "comment": "This preprint is an improved version of the previous preprint : \"A remark on the ill-posedness issues for KdV and mKdV \"",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove that the solution-map $ u_0 \\mapsto u $ associated with the KdV equation cannot be continuously extended in $ H^s(\\R) $ for $ s<-1 $. The main ingredients are the well-known Kato smoothing effect for the mKdV equation as well as the Miura transform.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-09-15T14:53:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ill-posedness",
      "well-known kato smoothing effect",
      "main ingredients",
      "miura transform",
      "mkdv equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.3133M"
    }
  }
}