{
  "id": "2005.00830",
  "version": "v1",
  "published": "2020-05-02T13:30:27.000Z",
  "updated": "2020-05-02T13:30:27.000Z",
  "title": "On the Navier-Stokes equations on surfaces",
  "authors": [
    "Jan Pruess",
    "Gieri Simonett",
    "Mathias Wilke"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the motion of an incompressible viscous fluid that completely covers a smooth, compact and embedded hypersurface $\\Sigma$ without boundary and flows along $\\Sigma$. Local-in-time well-posedness is established in the framework of $L_p$-$L_q$-maximal regularity. We characterize the set of equilibria as the set of all Killing vector fields on $\\Sigma$ and we show that each equilibrium on $\\Sigma$ is stable. Moreover, it is shown that any solution starting close to an equilibrium exists globally and converges at an exponential rate to a (possibly different) equilibrium as time tends to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-02T13:30:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "35Q30",
      "35B40"
    ],
    "keywords": [
      "navier-stokes equations",
      "equilibrium",
      "exponential rate",
      "solution starting close",
      "maximal regularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}