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Exponential convergence to the Maxwell distribution of solutions of spatially inhomogeneous Boltzmann equations

Gang, Zhou (2020) Exponential convergence to the Maxwell distribution of solutions of spatially inhomogeneous Boltzmann equations. Reviews in Mathematical Physics, 32 (1). Art. No. 2050001. ISSN 0129-055X. https://resolver.caltech.edu/CaltechAUTHORS:20200227-103331364

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Abstract

We consider the rate of convergence of solutions of spatially inhomogeneous Boltzmann equations, with hard-sphere potentials, to some equilibriums, called Maxwellians. Maxwellians are spatially homogeneous static Maxwell velocity distributions with different temperatures and mean velocities. We study solutions in weighted space L¹ (R³×T³). The result is that, assuming the solution is sufficiently localized and sufficiently smooth, then the solution, in L¹-space, converges to a Maxwellian, exponentially fast in time.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1142/s0129055x20500014DOIArticle
https://arxiv.org/abs/1603.06642arXivDiscussion Paper
Additional Information:© 2020 World Scientific Publishing Company. Received 1 September 2016; Revised 13 June 2019; Accepted 16 June 2019; Published 1 August 2019. Partly supported by NSF grants DMS-1308985 and DMS-1443225.
Funders:
Funding AgencyGrant Number
NSFDMS-1308985
NSFDMS-1443225
Subject Keywords:Boltzmann equation; Maxwelliana; symptotic
Issue or Number:1
Classification Code:Mathematics Subject Classification 2010: 76P05, 35Q70
Record Number:CaltechAUTHORS:20200227-103331364
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200227-103331364
Official Citation:Exponential convergence to the Maxwell distribution of solutions of spatially inhomogeneous Boltzmann equations. Zhou Gang. Reviews in Mathematical Physics 2020 32:01; doi: 10.1142/s0129055x20500014
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101614
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:27 Feb 2020 19:32
Last Modified:27 Feb 2020 19:32

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