Remarks on the acoustic limit for the Boltzmann equation

Ning Jiang, C. David Levermore, Nader Masmoudi

Research output: Contribution to journalArticlepeer-review


We improve in three ways the results of [6] that establish the acoustic limit for DiPerna-Lions solutions of Boltzmann equation. First, we enlarge the class of collision kernels treated to that found in [13], 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(εm) for some m > 1/2 to (ε1/2. Third, we extend the results from periodic domains to bounded domains with a Maxwell reflection boundary condition, deriving the impermeable boundary condition for the acoustic system.

Original languageEnglish (US)
Pages (from-to)1590-1609
Number of pages20
JournalCommunications in Partial Differential Equations
Issue number9
StatePublished - 2010


  • Acoustic limit
  • Boltzmann equation
  • Renormalized boundary condition

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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