{
  "id": "math/0611197",
  "version": "v1",
  "published": "2006-11-07T18:14:00.000Z",
  "updated": "2006-11-07T18:14:00.000Z",
  "title": "Well-posedness for the Kadomtsev-Petviashvili II equation and generalisations",
  "authors": [
    "M. Hadac"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show the local in time well-posedness of the Cauchy problem for the Kadomtsev-Petviashvili II equation for initial data in the non-isotropic Sobolev space H^{s_1,s_2}(R^2) with s_1 > -1/2 and s_2 \\geq 0. On the H^{s_1,0}(R^2) scale this result includes the full subcritical range without any additional low frequency assumption on the initial data. More generally, we prove the local in time well-posedness of the Cauchy problem for a dispersion generalised KP II type equation. We also deduce a global well-posedness result for the generalised equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-07T18:14:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q53",
      "35B30"
    ],
    "keywords": [
      "kadomtsev-petviashvili",
      "time well-posedness",
      "cauchy problem",
      "initial data",
      "generalisations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11197H"
    }
  }
}