{
  "id": "2008.01753",
  "version": "v1",
  "published": "2020-08-04T18:14:21.000Z",
  "updated": "2020-08-04T18:14:21.000Z",
  "title": "Global estimates for the Hartree-Fock-Bogoliubov equations",
  "authors": [
    "Jacky Jia Wei Chong",
    "Manoussos G. Grillakis",
    "Matei Machedon",
    "Zehua Zhao"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove that certain Sobolev-type norms, slightly stronger than those given by energy conservation, stay bounded uniformly in time and $N$. This allows one to extend the local existence results of the second and third author globally in time. The proof is based on interaction Morawetz-type estimates and Strichartz estimates (including some new end-point results) for the equation $\\{ \\frac{1}{i}\\partial_t-\\Delta_{x}-\\Delta_{y}+\\frac{1}{N}V_N(x-y) \\}\\Lambda(t, x, y) =F$ in mixed coordinates such as $L^p(dt) L^q(dx) L^2(dy)$, $L^p(dt) L^q(dy) L^2(dx)$, $L^p(dt) L^q(d(x-y)) L^2(d(x+y))$. The main new technical ingredient is a dispersive estimate in mixed coordinates, which may be of interest in its own right.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-04T18:14:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global estimates",
      "hartree-fock-bogoliubov equations",
      "local existence results",
      "interaction morawetz-type estimates",
      "mixed coordinates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}