{
  "id": "math/0701857",
  "version": "v3",
  "published": "2007-01-29T18:22:41.000Z",
  "updated": "2008-02-26T07:26:44.000Z",
  "title": "Loss of regularity for supercritical nonlinear Schrodinger equations",
  "authors": [
    "Thomas Alazard",
    "Rémi Carles"
  ],
  "comment": "More details in the computations. Additional remarks in Section 6",
  "journal": "Math. Ann. 343, 2 (2009) 397-420",
  "doi": "10.1007/s00208-008-0276-6",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the nonlinear Schrodinger equation with defocusing, smooth, nonlinearity. Below the critical Sobolev regularity, it is known that the Cauchy problem is ill-posed. We show that this is even worse: there is a loss of regularity, in the same spirit as the result due to G.Lebeau in the case of the wave equation. We use an isotropic change of variable, which reduces the problem to a super-critical WKB analysis. For super-cubic, smooth nonlinearity, this analysis is new, and relies on the introduction of a modulated energy functional a la Brenier.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-02-26T07:26:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A07",
      "35B33",
      "35B65",
      "35Q55",
      "76Y05",
      "81Q05",
      "81Q20"
    ],
    "keywords": [
      "supercritical nonlinear schrodinger equations",
      "sobolev regularity",
      "cauchy problem",
      "wave equation",
      "isotropic change"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1857A"
    }
  }
}