{
  "id": "2310.18731",
  "version": "v1",
  "published": "2023-10-28T15:25:28.000Z",
  "updated": "2023-10-28T15:25:28.000Z",
  "title": "Scattering and blow up for nonlinear Schrödinger equation with the averaged nonlinearity",
  "authors": [
    "Jumpei Kawakami"
  ],
  "comment": "42 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider 3-dimensional nonlinear Schr\\\"{o}dinger equation with an averaged nonlinearity. This is a generalized model of the resonant system of NLS with partial harmonic oscillator, in terms of the nonlinear power. We give a new proof for the conservation law of Kinetic energy and remove a restriction on the nonlinearity. Moreover, in the focusing, super-quintic, and sub-nonic case, we construct a ground state solution and classify the behavior of the solutions below the ground state. We show the sharp threshold for scattering and blow up.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-28T15:25:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55"
    ],
    "keywords": [
      "nonlinear schrödinger equation",
      "averaged nonlinearity",
      "partial harmonic oscillator",
      "scattering",
      "ground state solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}