{
  "id": "2201.02825",
  "version": "v1",
  "published": "2022-01-08T13:14:18.000Z",
  "updated": "2022-01-08T13:14:18.000Z",
  "title": "On the convergence from Boltzmann to Navier-Stokes-Fourier for general initial data",
  "authors": [
    "Pierre Gervais"
  ],
  "doi": "10.1137/22M1471687",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this work, we prove the convergence of strong solutions of the Boltzman equation, for initial data having polynomial decay in the velocity variable, towards those of the incompressible Navier-Stokes-Fourier system. We show in particular that the solutions of the rescaled Boltzmann equation do not blow up before their hydrodynamic limit does. This is made possible by adapting a strategy introduced by M. Briant, S. Merino and C. Mouhot of writing the solution to the Boltzmann equation as the sum a part with polynomial decay and a second one with Gaussian decay. The Gaussian part is treated with an approach reminiscent of the one used by I. Gallagher and I. Tristani.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-08T13:14:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82C40",
      "35B40",
      "35B45",
      "35B30"
    ],
    "keywords": [
      "general initial data",
      "convergence",
      "polynomial decay",
      "strong solutions",
      "incompressible navier-stokes-fourier system"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}