{
  "id": "math/0511492",
  "version": "v1",
  "published": "2005-11-19T23:36:34.000Z",
  "updated": "2005-11-19T23:36:34.000Z",
  "title": "Global well-posedness for a NLS-KdV system on $\\mathbb{T}$",
  "authors": [
    "Carlos Matheus"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove that the Cauchy problem of the Schr\\\"odinger - Korteweg - deVries (NLS-KdV) system on $\\mathbb{T}$ is globally well-posed for initial data $(u_0,v_0)$ below the energy space $H^1\\times H^1$. More precisely, we show that the non-resonant NLS-KdV is globally well-posed for initial data $(u_0,v_0)\\in H^s(\\mathbb{T})\\times H^s(\\mathbb{T})$ with $s>11/13$ and the resonant NLS-KdV is globally well-posed for initial data $(u_0,v_0)\\in H^s(\\mathbb{T})\\times H^s(\\mathbb{T})$ with $s>8/9$. The idea of the proof of this theorem is to apply the I-method of Colliander, Keel, Staffilani, Takaoka and Tao in order to improve the results of Arbieto, Corcho and Matheus concerning the global well-posedness of the NLS-KdV on $\\mathbb{T}$ in the energy space $H^1\\times H^1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-11-19T23:36:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q99"
    ],
    "keywords": [
      "global well-posedness",
      "nls-kdv system",
      "initial data",
      "energy space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....11492M"
    }
  }
}