Global Well-posedness of the Relativistic Boltzmann Equation

TL;DR

This paper establishes the global existence, uniqueness, and stability of solutions to the relativistic Boltzmann equation under certain initial conditions, advancing the mathematical understanding of relativistic kinetic theory.

Contribution

It proves the first comprehensive global well-posedness results for the relativistic Boltzmann equation in both whole space and torus settings with specific initial data conditions.

Findings

Global existence and uniqueness of solutions

Asymptotic stability in the torus case

Solutions depend continuously on initial data

Abstract

In this paper, we prove the global existence and uniqueness of mild solution to the relativistic Boltzmann equation both in the whole space and in torus for a class of initial data with bounded velocity-weighted $L^\infty$-norm and some smallness on $L^1_xL^\infty_p$-norm as well as on defect mass, energy and entropy. Moreover, the asymptotic stability of the solutions is also investigated in the case of torus.