{
  "id": "1305.4089",
  "version": "v1",
  "published": "2013-05-17T14:17:14.000Z",
  "updated": "2013-05-17T14:17:14.000Z",
  "title": "Large time behavior in nonlinear Schrodinger equation with time dependent potential",
  "authors": [
    "Rémi Carles",
    "Jorge Drumond Silva"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the large time behavior of solutions to defocusing nonlinear Schrodinger equation in the presence of a time dependent external potential. The main assumption on the potential is that it grows at most quadratically in space, uniformly with respect to the time variable. We show a general exponential control of first order derivatives and momenta, which yields a double exponential bound for higher Sobolev norms and momenta. On the other hand, we show that if the potential is an isotropic harmonic potential with a time dependent frequency which decays sufficiently fast, then Sobolev norms are bounded, and momenta grow at most polynomially in time, because the potential becomes negligible for large time: there is scattering, even though the potential is unbounded in space for fixed time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-17T14:17:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large time behavior",
      "time dependent potential",
      "time dependent external potential",
      "sobolev norms",
      "defocusing nonlinear schrodinger equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.4089C"
    }
  }
}