{
  "id": "1706.03491",
  "version": "v1",
  "published": "2017-06-12T07:19:06.000Z",
  "updated": "2017-06-12T07:19:06.000Z",
  "title": "Long range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity in three space dimensions",
  "authors": [
    "Satoshi Masaki",
    "Hayato Miyazaki",
    "Kota Uriya"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider the final state problem for the nonlinear Schr\\\"odinger equation with a homogeneous nonlinearity of the critical order which is not necessarily a polynomial. In [10], the first and the second authors consider one- and two-dimensional cases and gave a sufficient condition on the nonlinearity for that the corresponding equation admits a solution that behaves like a free solution with or without a logarithmic phase correction. The present paper is devoted to the study of the three-dimensional case, in which it is required that a solution converges to a given asymptotic profile in a faster rate than in the lower dimensional cases. To obtain the necessary convergence rate, we employ the end-point Strichartz estimate and modify a time-dependent regularizing operator, introduced in [10]. Moreover, we present a candidate of the second asymptotic profile to the solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-12T07:19:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B44",
      "35Q55",
      "35P25"
    ],
    "keywords": [
      "nonlinear schrödinger equations",
      "long range scattering",
      "critical homogeneous nonlinearity",
      "space dimensions",
      "final state problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}