Spectrum analysis for the relativistic Boltzmann equation

TL;DR

This paper analyzes the spectral properties of the linearized relativistic Boltzmann equation around a Maxwellian and uses this to determine optimal convergence rates for solutions.

Contribution

It provides a detailed spectrum analysis of the relativistic Boltzmann equation and establishes the best possible convergence rates for its solutions.

Findings

Spectral structure of the linearized relativistic Boltzmann operator characterized.

Optimal decay rates for solutions to the relativistic Boltzmann equation established.

Insights into the stability and long-time behavior of solutions obtained.

Abstract

The spectrum structure of the linearized relativistic Boltzmann equation around a global Maxwellian is studied in this paper. Based on the spectrum analysis, we establish the optimal time-convergence rates of the global solution to the Cauchy problem for the relativistic Boltzmann equation.