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The derivation of the linear Boltzmann equation from a Rayleigh gas particle model
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Matthies, Karsten, Stone, George and Theil, Florian (2018) The derivation of the linear Boltzmann equation from a Rayleigh gas particle model. Kinetic and Related Models, 11 (1). pp. 137-177. doi:10.3934/krm.2018008 ISSN 1937-5093.
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WRAP-derviation-linear-equation-Rayleigh-gas-particle-model-Theil-2018.pdf - Accepted Version - Requires a PDF viewer. Download (759Kb) | Preview |
Official URL: http://dx.doi.org/10.3934/krm.2018008
Abstract
A linear Boltzmann equation is derived in the Boltzmann-Grad scaling for the deterministic dynamics of many interacting particles with random initial data. We study a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions with background particles, which do not interact among each other. In the Boltzmann-Grad scaling, we derive the validity of a linear Boltzmann equation for arbitrary long times under moderate assumptions on higher moments of the initial distributions of the tagged particle and the possibly non-equilibrium distribution of the background. The convergence of the empiric dynamics to the Boltzmann dynamics is shown using Kolmogorov equations for associated probability measures on collision histories.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QC Physics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Transport theory, Rayleigh flow | ||||||
Journal or Publication Title: | Kinetic and Related Models | ||||||
Publisher: | American Institute of Mathematical Sciences | ||||||
ISSN: | 1937-5093 | ||||||
Official Date: | 1 February 2018 | ||||||
Dates: |
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Volume: | 11 | ||||||
Number: | 1 | ||||||
Page Range: | pp. 137-177 | ||||||
DOI: | 10.3934/krm.2018008 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 12 February 2018 | ||||||
Date of first compliant Open Access: | 1 February 2019 |
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