Derivation of kinetic and diffusion equations from a hard-sphere Rayleigh gas using collision trees and semigroups

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Abstract

We will revisit the classical questions of understanding the statistics of various deterministic dynamics of $N$ hard spheres of diameter $\varepsilon$ with random initial data in the Boltzmann-Grad scaling as $\varepsilon$ tends to zero and $N$ tends to infinity. The convergence of the empiric particle dynamics to the Boltzmann-type dynamics is shown using semigroup methods to describe probability measures on collision trees associated to physical trajectories in the case of a Rayleigh gas. As an application we derive the diffusion equation by a further rescaling.
Original languageEnglish
PublisherLondon Mathematical Society
Publication statusAcceptance date - 3 May 2024

Publication series

NameLondon Mathematical Society Lecture Note Series

Bibliographical note

To appear in LMS lecture notes for conference 'Dynamics, Bifurcations and Numerics', University of Surrey, July 2023

Keywords

  • math.AP
  • math.DS

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