{
  "id": "1009.2005",
  "version": "v4",
  "published": "2010-09-10T13:00:46.000Z",
  "updated": "2012-02-10T02:10:44.000Z",
  "title": "Continuous Dependence of Cauchy Problem For Nonlinear Schrödinger Equation in $H^{s}$",
  "authors": [
    "Wei Dai",
    "Weihua Yang",
    "Daomin Cao"
  ],
  "comment": "48pages, no figure. arXiv admin note: text overlap with arXiv:1006.2745 by other authors",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the Cauchy problem for the nonlinear Schr\\\"{o}dinger equation $i \\partial_{t}u+ \\Delta u=\\lambda_{0}u+\\lambda_{1}|u|^\\alpha u$ in $\\mathbb{R}^{N}$, where $\\lambda_{0},\\lambda_{1}\\in\\mathbb{C}$, in $H^s$ subcritical and critical case: $0<\\alpha\\leq\\frac{4}{N-2s}$ when $1<s<\\frac{N}{2}$ and $0<\\alpha<+\\infty$ when $s\\geq\\frac{N}{2}$. We show that the solution depends continuously on the initial value in the standard sense in $H^{s}(\\mathbb{R}^{N})$ if $\\alpha$ satisfies certain assumptions.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-02-10T02:10:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55"
    ],
    "keywords": [
      "nonlinear schrödinger equation",
      "cauchy problem",
      "continuous dependence",
      "initial value",
      "standard sense"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.2005D"
    }
  }
}