Exponential convergence to the Maxwell distribution for some class of Boltzmann equations
type: Item
instance of: scholarly article
title: Exponential convergence to the Maxwell distribution for some class of Boltzmann equations
zbMATH Open document ID: 1270.35100
author: Jürg Fröhlich
author: Zhou Gang
published in: Communications in Mathematical Physics
publication date: 2012-09-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/1011.4194
full work available at URL: http://hdl.handle.net/20.500.11850/54608
review text: This paper concerns a class of nonlinear Boltzmann equations describing return to thermal equilibrium in a gas of colliding particles suspended in a thermal medium. It is proved that, in a three-dimensional flat torus, and for sufficiently small values of the mole number of the gas, the solutions with smooth initial datum in a weighted \(L^1\)-space converges to the global Maxwellian in an \(L^1\)-space, exponentially fast in time. The authors' argument mainly uses perturbation theory to prove decay estimates for propagators.
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 76P05
Mathematics Subject Classification ID: 35Q20
Mathematics Subject Classification ID: 35P30
Mathematics Subject Classification ID: 82C40
Mathematics Subject Classification ID: 35Q61
zbMATH DE Number: 6084015
zbMATH Keywords: torus domain
zbMATH Keywords: exponential convergence
zbMATH Keywords: nonlinear Boltzmann equations
MaRDI profile type: Publication
OpenAlex ID: W2963456120
arXiv ID: 1011.4194
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DOI: 10.1007/S00220-012-1499-7
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