{
  "id": "0902.1982",
  "version": "v1",
  "published": "2009-02-11T21:04:31.000Z",
  "updated": "2009-02-11T21:04:31.000Z",
  "title": "Local well-posedness results for density-dependent incompressible fluids",
  "authors": [
    "Boris Haspot"
  ],
  "journal": "Annales de l'Institut Fourier}, 62 (5) (2012) p. 1717-1763",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is dedicated to the study of the initial value problem for density dependent incompressible viscous fluids in $\\R^{N}$ with $N\\geq2$. We address the question of well-posedness for {\\it large} data having critical Besov regularity and we aim at stating well-posedness in functional spaces as close as possible to the ones imposed in the incompressible Navier Stokes system by Cannone, Meyer and Planchon where $u_{0}\\in B^{\\NN-1}_{p,\\infty}$ with $1\\leq p<+\\infty$. This improves the analysis of H. Abidi, R. Danchin and M. Paicu where $u_{0}$ is considered belonging to $B^{\\NN-1}_{p,1}$ with $1\\leq p<2N$. Our result relies on a new a priori estimate for transport equation introduce by Bahouri, Chemin and Danchin when the velocity $u$ is not considered Lipschitz.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-11T21:04:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local well-posedness results",
      "density-dependent incompressible fluids",
      "density dependent incompressible viscous fluids",
      "initial value problem",
      "incompressible navier stokes system"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.1982H"
    }
  }
}