{
  "id": "math/0701858",
  "version": "v1",
  "published": "2007-01-29T18:23:18.000Z",
  "updated": "2007-01-29T18:23:18.000Z",
  "title": "On the instability for the cubic nonlinear Schrodinger equation",
  "authors": [
    "Rémi Carles"
  ],
  "comment": "4 pages",
  "journal": "C. R. Math. Acad. Sci. Paris 344, 8 (2007) 483-486",
  "doi": "10.1016/j.crma.2007.03.006",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the flow map associated to the cubic Schrodinger equation in space dimension at least three. We consider initial data of arbitrary size in $H^s$, where $0<s<s_c$, $s_c$ the critical index, and perturbations in $H^\\si$, where $\\si<s_c$ is independent of $s$. We show an instability mechanism in some Sobolev spaces of order smaller than $s$. The analysis relies on two features of super-critical geometric optics: creation of oscillation, and ghost effect.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-01-29T18:23:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B33",
      "35B65",
      "35Q55",
      "81Q05",
      "81Q20"
    ],
    "keywords": [
      "cubic nonlinear schrodinger equation",
      "cubic schrodinger equation",
      "sobolev spaces",
      "space dimension",
      "initial data"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1858C"
    }
  }
}