The Derivation of the Linear Boltzmann Equation from a Rayleigh Gas Particle Model

Autor:	Matthies, Karsten, Stone, George, Theil, Florian
Rok vydání:	2016
Předmět:	Mathematics - Analysis of PDEs Mathematical Physics
Zdroj:	Kinetic and Related Models 11 (2018), 137 - 177
Druh dokumentu:	Working Paper
DOI:	10.3934/krm.2018008
Popis:	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. Comment: minor corrections
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1603.07574 Zobrazit plný text záznamu View this record from Arxiv