Projects per year
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 BoltzmannGrad scaling as $\varepsilon$ tends to zero and $N$ tends to infinity. The convergence of the empiric particle dynamics to the Boltzmanntype 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 language  English 

Publisher  London Mathematical Society 
Publication status  Acceptance date  3 May 2024 
Publication series
Name  London Mathematical Society Lecture Note Series 

Bibliographical note
To appear in LMS lecture notes for conference 'Dynamics, Bifurcations and Numerics', University of Surrey, July 2023Keywords
 math.AP
 math.DS
Projects
 1 Finished

Derivation of kinetic equation: From Newton to Boltzmann via trees
1/10/20 → 31/03/24
Project: UK charity