{
  "id": "1712.05211",
  "version": "v1",
  "published": "2017-12-14T13:15:58.000Z",
  "updated": "2017-12-14T13:15:58.000Z",
  "title": "Cauchy problem for the incompressible Navier-Stokes equation with an external force",
  "authors": [
    "Di Wu"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper we focus on the Cauchy problem for the incompressible Navier-Stokes equation with a rough external force. If the given rough external force is small, we prove the local-in-time existence of this system for any initial data belonging to the critical Besov space $\\dot{B}_{p,p}^{-1+\\frac{3}{p}}$, where $3<p<\\infty$. Moreover, We show the long-time behavior of the priori global solutins constructed by us. Also, we give three kinds of uniqueness results of the forced Navier-Stokes equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-14T13:15:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "35B35",
      "35B40",
      "35B20"
    ],
    "keywords": [
      "incompressible navier-stokes equation",
      "cauchy problem",
      "rough external force",
      "priori global solutins",
      "forced navier-stokes equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}