The acoustic limit for the Boltzmann equation
type: Item
instance of: scholarly article
title: The acoustic limit for the Boltzmann equation
zbMATH Open document ID: 0973.76075
author: C. Bardos
author: François Golse
author: C. David Levermore
published in: Archive for Rational Mechanics and Analysis
publication date: 2001-12-05T00:00:00Z
review text: First, the authors derive acoustic equations directly from the Boltzmann equation as a formal limit of moment equations for an appropriately scaled family of Boltzmann solutions. Then this limit is investigated for the Boltzmann equation considered over a periodic spatial domain for bounded collision kernels. Appropriately scaled families of Di Perma-Lions renormalized solutions are shown to have fluctuations that converge entropically to a unique limit described by a solution of acoustic equations for all time, provided that its initial fluctuations converge entropically to an limit associated to any given \(L^2\) initial data of acoustic equations. The associated local conservation laws are recovered in this limit.
Mathematics Subject Classification ID: 76P05
Mathematics Subject Classification ID: 76A02
Mathematics Subject Classification ID: 45K05
zbMATH DE Number: 1501924
zbMATH Keywords: L(2) initial data
zbMATH Keywords: acoustic equations
zbMATH Keywords: Boltzmann equation
zbMATH Keywords: limit of moment equations
zbMATH Keywords: bounded collision kernels
zbMATH Keywords: Di Perma-Lions renormalized solutions
zbMATH Keywords: fluctuations
zbMATH Keywords: local conservation laws
reviewed by: Agneta M. Balint
MaRDI profile type: Publication
full work available at URL: s002050000080
OpenAlex ID: W2024232953
DOI: 10.1007/S002050000080
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description: scientific article; zbMATH DE number 1501924