{
  "id": "2101.05157",
  "version": "v1",
  "published": "2021-01-13T15:55:43.000Z",
  "updated": "2021-01-13T15:55:43.000Z",
  "title": "Concentration versus absorption for the Vlasov-Navier-Stokes system on bounded domains",
  "authors": [
    "Lucas Ertzbischoff",
    "Daniel Han-Kwan",
    "Ayman Moussa"
  ],
  "comment": "55 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the large time behavior of small data solutions to the Vlasov-Navier-Stokes system set on $\\Omega \\times \\mathbb{R}^3$, for a smooth bounded domain $\\Omega$ of $\\mathbb{R}^3$, with homogeneous Dirichlet boundary condition for the fluid and absorption boundary condition for the kinetic phase. We prove that the fluid velocity homogenizes to $0$ while the distribution function concentrates towards a Dirac mass in velocity centered at $0$, with an exponential rate. The proof, which follows the methods introduced in [Han-Kwan - Moussa - Moyano, arXiv:1902.03864v2], requires a careful analysis of the boundary effects. We also exhibit examples of classes of initial data leading to a variety of asymptotic behaviors for the kinetic density, from total absorption to no absorption at all.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-13T15:55:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "concentration",
      "vlasov-navier-stokes system set",
      "distribution function concentrates",
      "homogeneous dirichlet boundary condition",
      "small data solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}