{
  "id": "0903.5086",
  "version": "v2",
  "published": "2009-03-29T19:30:51.000Z",
  "updated": "2010-05-25T00:02:44.000Z",
  "title": "Remarks on the Acoustic Limit for the Boltzmann Equation",
  "authors": [
    "Ning Jiang",
    "C. David Levermore",
    "Nader Masmoudi"
  ],
  "comment": "17 pages",
  "journal": "Communications in Partial Differential Equations 2010",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We use some new nonlinear estimates found in \\cite {LM} to improve the results of \\cite{GL} that establish the acoustic limit for DiPerna-Lions solutions of Boltzmann equation in three ways. First, we enlarge the class of collision kernels treated to that found in \\cite{LM}, thereby treating all classical collision kernels to which the DiPerna-Lions theory applies. Second, we improve the scaling of the kinetic density fluctuations with Knudsen number from $O(\\epsilon^m)$ for some $m>\\frac12$ to $O(\\epsilon^\\frac12)$. Third, we extend the results from periodic domains to bounded domains with impermeable boundaries, deriving the boundary condition for the acoustic system.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-05-25T00:02:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "acoustic limit",
      "boltzmann equation",
      "diperna-lions theory applies",
      "kinetic density fluctuations",
      "acoustic system"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.5086J"
    }
  }
}