Propagation of chaos for the spatially homogeneous Landau equation for Maxwellian molecules

TL;DR

This paper establishes a uniform-in-time propagation of chaos for the spatially homogeneous Landau equation with Maxwellian molecules, improving previous finite-time results and providing convergence rates to equilibrium.

Contribution

It extends propagation of chaos results to infinite time and offers quantitative convergence rates, advancing understanding of particle system limits for the Landau equation.

Findings

Uniform-in-time propagation of chaos proved

Quantitative convergence rates to equilibrium established

Improved upon previous finite-time results

Abstract

We prove a quantitative propagation of chaos, uniformly in time, for the spatially homogeneous Landau equation in the case of Maxwellian molecules. We improve the results of Fontbona, Gu\'erin and M\'el\'eard \cite{FonGueMe} and Fournier \cite{Fournier} where the propagation of chaos is proved for finite time. Moreover, we prove a quantitative estimate on the rate of convergence to equilibrium uniformly in the number of particles.