Remarks on the acoustic limit for the Boltzmann equation

Ning Jiang, C. David Levermore, Nader Masmoudi

Research output: Contribution to journalArticle

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

Fingerprint

Boltzmann equation
Boltzmann Equation
Acoustics
Collision
Boundary conditions
kernel
Knudsen number
Bounded Domain
Kinetics
Scaling
Fluctuations
Class

Keywords

  • Acoustic limit
  • Boltzmann equation
  • Renormalized boundary condition

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Remarks on the acoustic limit for the Boltzmann equation. / Jiang, Ning; Levermore, C. David; Masmoudi, Nader.

In: Communications in Partial Differential Equations, Vol. 35, No. 9, 2010, p. 1590-1609.

Research output: Contribution to journalArticle

Jiang, Ning ; Levermore, C. David ; Masmoudi, Nader. / Remarks on the acoustic limit for the Boltzmann equation. In: Communications in Partial Differential Equations. 2010 ; Vol. 35, No. 9. pp. 1590-1609.
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