Spatially homogeneous Maxwellian molecules in a neighborhood of the equilibrium

TL;DR

This paper studies the exponential convergence to equilibrium for the spatially homogeneous Boltzmann equation with Maxwellian molecules, providing a quantification of the convergence rate for initial data near equilibrium.

Contribution

It offers a simple method to quantify the exponential convergence rate of solutions close to Maxwellian equilibrium in the spatially homogeneous Boltzmann equation for Maxwellian molecules.

Findings

Exponential convergence rate is quantified.

Results apply to initial data near equilibrium.

Method is based on simple arguments.

Abstract

This note deals with the long-time behavior of the solution to the spatially homogeneous Boltzmann equation for Maxwellian molecules, when the initial datum belongs to a suitable neighborhood of the Maxwellian equilibrium. In particulary, it contains a quantification of the rate of exponential convergence, obtained by simple arguments.