Remarks on the acoustic limit for the Boltzmann equation

Ning Jiang, C. David Levermore, Nader Masmoudi

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume35
Issue number9
DOIs
StatePublished - 2010

Keywords

  • Acoustic limit
  • Boltzmann equation
  • Renormalized boundary condition

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Remarks on the acoustic limit for the Boltzmann equation'. Together they form a unique fingerprint.

Cite this