{
  "id": "0909.0794",
  "version": "v2",
  "published": "2009-09-04T01:49:06.000Z",
  "updated": "2009-12-12T00:23:36.000Z",
  "title": "Weak Continuity of Dynamical Systems for the KdV and mKdV Equations",
  "authors": [
    "Shangbin Cui",
    "Carlos E. Kenig"
  ],
  "comment": "21 pages, no figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study weak continuity of the dynamical systems for the KdV equation in H^{-3/4}(R) and the modified KdV equation in H^{1/4}(R). This topic should have significant applications in the study of other properties of these equations such as finite time blow-up and asymptotic stability and instability of solitary waves. The spaces considered here are borderline Sobolev spaces for the corresponding equations from the viewpoint of the local well-posedness theory. We first use a variant of the method of [5] to prove weak continuity for the mKdV, and next use a similar result for a mKdV system and the generalized Miura transform to get weak continuity for the KdV equation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-12-12T00:23:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L70"
    ],
    "keywords": [
      "dynamical systems",
      "mkdv equations",
      "finite time blow-up",
      "study weak continuity",
      "borderline sobolev spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.0794C"
    }
  }
}