{
  "id": "1402.5251",
  "version": "v1",
  "published": "2014-02-21T11:10:43.000Z",
  "updated": "2014-02-21T11:10:43.000Z",
  "title": "Global Attractor for the Navier-Stokes Equations with horizontal filtering",
  "authors": [
    "Luca Bisconti",
    "Davide Catania"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a Large Eddy Simulation model for a homogeneous incompressible Newtonian fluid in a box space domain with periodic boundary conditions on the lateral boundaries and homogeneous Dirichlet conditions on the top and bottom boundaries, thus simulating a horizontal channel. The model is obtained through the application of an anisotropic horizontal filter, which is known to be less memory consuming from a numerical point of view, but provides less regularity with respect to the standard isotropic one defined as the inverse of the Helmholtz operator. It is known that there exists a unique regular weak solution to this model that depends weakly continuously on the initial datum. We show the existence of the global attractor for the semiflow given by the time-shift in the space of paths. We prove the continuity of the horizontal components of the flow under periodicity in all directions and discuss the possibility to introduce a solution semiflow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-21T11:10:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global attractor",
      "navier-stokes equations",
      "unique regular weak solution",
      "large eddy simulation model",
      "anisotropic horizontal filter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.5251B"
    }
  }
}