{
  "id": "1009.5726",
  "version": "v2",
  "published": "2010-09-29T01:02:01.000Z",
  "updated": "2010-10-05T13:47:10.000Z",
  "title": "Global solutions for the generalized Boussinesq equation in low-order Sobolev spaces",
  "authors": [
    "Luiz Gustavo Farah",
    "Hongwei Wang"
  ],
  "comment": "13 pages. References updated",
  "journal": "Electronic Journal of Differential Equations, Vol. 2012 (2012), No. 41, pp. 1-13",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that the Cauchy problem for the defocusing generalized Boussinesq equation $u_{tt}-u_{xx}+u_{xxxx}-(|u|^{2k}u)_{xx}=0$, $k\\geq1$, on the real line is globally well-posed in $H^{s}(\\R)$ for $s>1-({1}/{3k})$. We use the \"$I$-method\" to define a modification of the energy functional that is \"almost conserved\" in time. Our result extends the previous one obtained by Farah and Linares (2010 \\textit{J. London Math. Soc.} \\textbf{81} 241-254) when $k=1$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-10-05T13:47:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B30",
      "35Q55",
      "35Q72"
    ],
    "keywords": [
      "low-order sobolev spaces",
      "global solutions",
      "london math",
      "cauchy problem",
      "result extends"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.5726F"
    }
  }
}