{
  "id": "2107.02200",
  "version": "v1",
  "published": "2021-07-05T18:04:24.000Z",
  "updated": "2021-07-05T18:04:24.000Z",
  "title": "Decay and absorption for the Vlasov-Navier-Stokes system with gravity in a half-space",
  "authors": [
    "Lucas Ertzbischoff"
  ],
  "comment": "53 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is devoted to the large time behavior of weak solutions to the three-dimensional Vlasov-Navier-Stokes system set on the half-space, with an external gravity force. This fluid-kinetic coupling arises in the modeling of sedimentation phenomena. We prove that the local density of the particles and the fluid velocity enjoy a convergence to $0$ in large time and at a polynomial rate. In order to overcome the effect of the gravity, we rely on a fine analysis of the absorption phenomenon at the boundary. We obtain a family of decay estimates for the moments of the kinetic distribution, provided that the initial distribution function has a sufficient decay in the phase space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-05T18:04:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "half-space",
      "absorption",
      "three-dimensional vlasov-navier-stokes system set",
      "external gravity force",
      "initial distribution function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}