{
  "id": "1908.01038",
  "version": "v1",
  "published": "2019-08-02T20:13:45.000Z",
  "updated": "2019-08-02T20:13:45.000Z",
  "title": "Orbital Stability of Standing Waves for Fractional Hartree Equation with Unbounded Potentials",
  "authors": [
    "Jian Zhang",
    "Shijun Zheng",
    "Shihui Zhu"
  ],
  "comment": "11 pages",
  "journal": "Contemporary Mathematics 2019; Volume 725. ISBN: 978-1-4704-4109-8",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove the existence of the set of ground states in a suitable energy space $\\Sigma^s=\\{u: \\int_{\\mathbb{R}^N} \\bar{u}(-\\Delta+m^2)^s u+V |u|^2<\\infty\\}$, $s\\in (0,\\frac{N}{2})$ for the mass-subcritical nonlinear fractional Hartree equation with unbounded potentials. As a consequence we obtain, as a priori result, the orbital stability of the set of standing waves. The main ingredient is the observation that $\\Sigma^s$ is compactly embedded in $L^2$. This enables us to apply the concentration compactness argument in the works of Cazenave-Lions and Zhang, namely, relative compactness for any minimizing sequence in the energy space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-02T20:13:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55"
    ],
    "keywords": [
      "orbital stability",
      "standing waves",
      "unbounded potentials",
      "mass-subcritical nonlinear fractional hartree equation",
      "energy space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}