{
  "id": "1005.0706",
  "version": "v1",
  "published": "2010-05-05T09:08:48.000Z",
  "updated": "2010-05-05T09:08:48.000Z",
  "title": "Existence of global strong solutions in critical spaces for barotropic viscous fluids",
  "authors": [
    "Boris Haspot"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is dedicated to the study of viscous compressible barotropic fluids in dimension $N\\geq2$. We address the question of the global existence of strong solutions for initial data close from a constant state having critical Besov regularity. In a first time, this article show the recent results of \\cite{CD} and \\cite{CMZ} with a new proof. Our result relies on a new a priori estimate for the velocity, where we introduce a new structure to \\textit{kill} the coupling between the density and the velocity as in \\cite{H2}. We study so a new variable that we call effective velocity. In a second time we improve the results of \\cite{CD} and \\cite{CMZ} by adding some regularity on the initial data in particular $\\rho_{0}$ is in $H^{1}$. In this case we obtain global strong solutions for a class of large initial data on the density and the velocity which in particular improve the results of D. Hoff in \\cite{5H4}. We conclude by generalizing these results for general viscosity coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-05T09:08:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global strong solutions",
      "barotropic viscous fluids",
      "critical spaces",
      "initial data close",
      "large initial data"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00205-011-0430-2",
      "journal": "Archive for Rational Mechanics and Analysis",
      "year": 2011,
      "month": "Nov",
      "volume": 202,
      "number": 2,
      "pages": 427
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011ArRMA.202..427H"
    }
  }
}