Convergence to Equilibrium of Some Kinetic Models

TL;DR

This paper presents a novel method to analyze the convergence to equilibrium in kinetic models, establishing conditions for exponential or polynomial rates even in degenerate or hypocoercive systems.

Contribution

It introduces a new approach based on weak coercive estimates that effectively handles hypocoercive and linearized Boltzmann equations.

Findings

Proves exponential or polynomial convergence rates.

Applicable to hypocoercive systems with degenerate coercive parts.

Effective for linearized Boltzmann equation.

Abstract

We introduce in this paper a new approach to the problem of the convergence to equilibrium for kinetic equations. The idea of the approach is to prove a 'weak' coercive estimate, which implies exponential or polynomial convergence rate. Our method works very well not only for hypocoercive systems in which the coercive parts are degenerate but also for the linearized Boltzmann equation.