{
  "id": "1610.06030",
  "version": "v1",
  "published": "2016-10-19T14:29:10.000Z",
  "updated": "2016-10-19T14:29:10.000Z",
  "title": "Improved nonrelativistic limit for ground states of the Schrödinger and Hartree equations",
  "authors": [
    "Woocheol Choi",
    "Younghun Hong",
    "Jinmyoung Seok"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Lenzmann \\cite{L2} and Choi-Seok \\cite{CS} proved that the ground states of the pseudo-relativistic Schr\\\"odinger equation with Hartree nonlinearity or power type nonlinearity \\[ \\big(\\sqrt{-c^2 \\Delta +\\tfrac{c^4}{4}} - \\tfrac{c^2}{2} \\big) u + \\mu u = \\mathcal{N}(u) \\] converges in $H^1 (\\mathbb{R}^n)$ to the ground state $u_{\\infty}$ of the nonrelativistic limit equation \\[ -\\Delta u + \\mu u = \\mathcal{N}(u). \\] In this paper, we improve these results by showing the convergence in higher order Sobolev spaces with an explicit convergence rate given by $1/c^2$, which turns out to be optimal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-19T14:29:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ground state",
      "hartree equations",
      "higher order sobolev spaces",
      "schrödinger",
      "nonrelativistic limit equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}