Small mass ratio limit of Boltzmann equations in the Context of the study of evolution of dust particles in a rarefied atmosphere
type: Item
instance of: scholarly article
title: Small mass ratio limit of Boltzmann equations in the Context of the study of evolution of dust particles in a rarefied atmosphere
zbMATH Open document ID: 1236.82053
author: Frédérique Charles
author: Laurent Desvillettes
published in: Journal of Statistical Physics
publication date: 2010-01-08T00:00:00Z
review text: The paper analyzes the evolution of particles of a dust in a rarefied atmosphere. This topic can be found in the context of safety studies for the ITER project of nuclear fusion. When the typical size of a dust particle becomes too large compared to that of a molecule of the gas, the corresponding numerical simulation becomes too expensive. Consequently, one needs to introduce an asymptotic model, in which the ratio of the gas-molecule mass to the dust-particle mass tends to zero. In order to obtain such a model, the paper considers a system of two Boltzmann equations for the distribution function of the gas molecules and distribution function of the dust particles. The latter function depends not only on the position and velocity but also on the particle radius, which can vary in a certain interval. The main result of the work is that, when the proposed model is spatially homogeneous, the model is, in the aforementioned limit case, reduced to a system of two equations of the Vlasov-Boltzmann type. The system is simpler and admits more effective numerical treatment. The passage to the limit is rigorously proven. The proof includes a new version of Povzner's inequality in which the vanishing mass ratio is taken into account.
reviewed by: Eugen Mamontov
Mathematics Subject Classification ID: 82C40
Mathematics Subject Classification ID: 82D05
Mathematics Subject Classification ID: 76P05
zbMATH DE Number: 5655379
zbMATH Keywords: Boltzmann equation
zbMATH Keywords: Vlasov equation
zbMATH Keywords: asymptotic model
zbMATH Keywords: Povzner's inequality
MaRDI profile type: Publication
full work available at URL: s10955-009-9858-2
OpenAlex ID: W2061023504
cites work: On the Boltzmann equation. II: The full initial value problem
cites work: Q4188953
cites work: Moment inequalities for the Boltzmann equation and applications to spatially homogneous problems
cites work: The Boltzmann equation and its applications
cites work: Measure solutions of the steady Boltzmann equation in a slab
cites work: THE ASYMPTOTICS OF COLLISION OPERATORS FOR TWO SPECIES OF PARTICLES OF DISPARATE MASSES
cites work: Transport coefficients of plasmas and disparate mass binary gases
cites work: Some applications of the method of moments for the homogeneous Boltzmann and Kac equations
cites work: About \(L^p\) estimates for the spatially homogeneous Boltzmann equation
cites work: A particle scheme for the numerical solution of the Enskog equation
cites work: On the Boltzmann equation for diffusively excited granular media
cites work: Conservation of energy, entropy identity, and local stability for the spatially homogeneous Boltzmann equation
cites work: On the spatially homogeneous Boltzmann equation
cites work: Q3754354
cites work: Q5336200
cites work: Entropy dissipation and moment production for the Boltzmann equation
DOI: 10.1007/S10955-009-9858-2
description: scientific article; zbMATH DE number 5655379