{
  "id": "1009.4538",
  "version": "v1",
  "published": "2010-09-23T08:13:28.000Z",
  "updated": "2010-09-23T08:13:28.000Z",
  "title": "Navier-Stokes equations on the $β$-plane",
  "authors": [
    "Mustafa Al-Jaboori",
    "Djoko Wirosoetisno"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that, given a sufficiently regular forcing, the solution of the two-dimensional Navier--Stokes equations on the periodic $\\beta$-plane (i.e.\\ with the Coriolis force varying as $f_0+\\beta y$) will become nearly zonal: with the vorticity $\\omega(x,y,t)=\\wb(y,t)+\\wt(x,y,t)$, one has $|\\wt|_{H^s}^2\\le\\beta^{-1} M_s(\\...)$ as $t\\to\\infty$. We use this show that, for sufficiently large $\\beta$, the global attractor of this system reduces to a point.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-23T08:13:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35B41",
      "76D05"
    ],
    "keywords": [
      "two-dimensional navier-stokes equations",
      "coriolis force",
      "global attractor",
      "system reduces",
      "sufficiently regular"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.4538A"
    }
  }
}