Abstract:
The acoustic equations are the linearization of the compressible Euler equations about a spatially homogeneous fluid state. We first derive them directly from the Boltzmann equation as the formal limit of moment equations for an appropriately scaled family of Boltzmann solutions. We then establish this limit for the Boltzmann equation considered over a periodic spatial domain for bounded collision kernels. Appropriately scaled families of DiPerna-Lions renormalized solutions are shown to have fluctuations that converge entropically (and hence strongly in L 1) to a unique limit governed by a solution of the acoustic equations for all time, provided that its initial fluctuations converge entropically to an appropriate limit associated to any given L 2 initial data of the acoustic equations. The associated local conservation laws are recovered in the limit.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Accepted: October 22, 1999
Rights and permissions
About this article
Cite this article
Bardos, C., Golse, F. & Levermore, C. The Acoustic Limit for the Boltzmann Equation. Arch. Rational Mech. Anal. 153, 177–204 (2000). https://doi.org/10.1007/s002050000080
Issue Date:
DOI: https://doi.org/10.1007/s002050000080