{
  "id": "2003.01468",
  "version": "v1",
  "published": "2020-03-03T12:06:22.000Z",
  "updated": "2020-03-03T12:06:22.000Z",
  "title": "Scattering for the mass-critical nonlinear Klein-Gordon equations in three and higher dimensions",
  "authors": [
    "Xing Cheng",
    "Zihua Guo",
    "Satoshi Masaki"
  ],
  "comment": "33 pages, no figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we consider the real-valued mass-critical nonlinear Klein-Gordon equations in three and higher dimensions. We prove the dichotomy between scattering and blow-up below the ground state energy in the focusing case, and the energy scattering in the defocusing case. We use the concentration-compactness/rigidity method as R. Killip, B. Stovall, and M. Visan [Trans. Amer. Math. Soc. 364 (2012)]. The main new novelty is to approximate the large scale (low-frequency) profile by the solution of the mass-critical nonlinear Schr\\\"odinger equation when the nonlinearity is not algebraic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-03T12:06:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L71",
      "35Q40",
      "35P25",
      "35B40"
    ],
    "keywords": [
      "higher dimensions",
      "scattering",
      "real-valued mass-critical nonlinear klein-gordon equations",
      "ground state energy",
      "concentration-compactness/rigidity method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}