{
  "id": "math/0204014",
  "version": "v1",
  "published": "2002-03-31T23:02:09.000Z",
  "updated": "2002-03-31T23:02:09.000Z",
  "title": "KdV and Almost Conservation Laws",
  "authors": [
    "Gigliola Staffilani"
  ],
  "comment": "15 pages. This paper will appear in the AMS Proceedings of the Conference on Harmonic Analysis held at Mt. Holyoke College, June 24 - July 5, 2001",
  "categories": [
    "math.AP"
  ],
  "abstract": "This short survey paper is concerned with a new method to prove global well-posedness results for dispersive equations below energy spaces, namely $H^{1}$ for the Schr\\\"odinger equation and $L^{2}$ for the KdV equation. The main ingredient of this method is the definition of a family of what we call almost conservation laws. In particular we analyze the Korteweg-de Vries initial value problem and we illustrate in general terms how the ``algorithm'' that we use to formally generate almost conservation laws can be used to recover the infinitely many conserved integrals that make the KdV an integrable system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-03-31T23:02:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q53",
      "42B35",
      "37K10"
    ],
    "keywords": [
      "conservation laws",
      "korteweg-de vries initial value problem",
      "global well-posedness results",
      "short survey paper",
      "energy spaces"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......4014S"
    }
  }
}