{
  "id": "1610.03479",
  "version": "v1",
  "published": "2016-10-11T19:53:16.000Z",
  "updated": "2016-10-11T19:53:16.000Z",
  "title": "On the Global Stability of a Beta-Plane Equation",
  "authors": [
    "Fabio Pusateri",
    "Klaus Widmayer"
  ],
  "comment": "35 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the motion of an incompressible, inviscid two-dimensional fluid in a rotating frame of reference. There the fluid experiences a Coriolis force, which we assume to be linearly dependent on one of the coordinates. This is a common approximation in geophysical fluid dynamics and is referred to as beta-plane. In vorticity formulation the model we consider is then given by the Euler equation with the addition of a linear anisotropic, non-degenerate, dispersive term. This allows us to treat the problem as a quasilinear dispersive equation whose linear solutions exhibit decay in time at a critical rate. Our main result is the global stability and decay to equilibrium of sufficiently small and localized solutions. Key aspects of the proof are the exploitation of a \"double null form\" that annihilates interactions between spatially coherent waves and a lemma for Fourier integral operators which allows us to control a strong weighted norm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-11T19:53:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global stability",
      "beta-plane equation",
      "inviscid two-dimensional fluid",
      "fourier integral operators",
      "fluid experiences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}