{
  "id": "1703.01609",
  "version": "v1",
  "published": "2017-03-05T15:25:55.000Z",
  "updated": "2017-03-05T15:25:55.000Z",
  "title": "Long time behaviour of the nonlinear Klein-Gordon equation in the nonrelativistic limit, I",
  "authors": [
    "Stefano Pasquali"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the the nonlinear Klein-Gordon (NLKG) equation on a manifold $M$ in the nonrelativistic limit, namely as the speed of light $c$ tends to infinity. In particular, we consider a higher-order normalized approximation of NLKG (which corresponds to the NLS at order $r=1$), and prove that when $M$ is a smooth compact manifold or $\\mathbb{R}^d$, the solution of the approximating equation approximates the solution of the NLKG locally uniformly in time. When $M=\\mathbb{R}^d$, $d \\geq 3$, we prove that small radiation solutions of the order $r$ normalized equation approximate solutions of NLKG up to times of order $\\mathcal{O}(c^{2(r-1)})$ for any $r>1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-05T15:25:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear klein-gordon equation",
      "long time behaviour",
      "nonrelativistic limit",
      "normalized equation approximate solutions",
      "small radiation solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}