Large-Time Decay of the Soft Potential relativistic Boltzmann equation in $\R^3_x$

TL;DR

This paper establishes the global existence, uniqueness, positivity, and optimal decay rates of solutions to the relativistic Boltzmann equation with soft potentials in three-dimensional space, advancing understanding of relativistic kinetic theory.

Contribution

It proves the first comprehensive results on global solutions and decay rates for the relativistic Boltzmann equation with soft potentials in D, under general physical assumptions.

Findings

Global existence and uniqueness of solutions

Optimal decay rates to relativistic Maxwellian

Solutions remain positive over time

Abstract

For the relativistic Boltzmann equation in $\R^3_x$, this work proves the global existence, uniqueness, positivity, and optimal time convergence rates to the relativistic Maxwellian for solutions which start out sufficiently close under the general physical soft potential assumption proposed in 1988 by Dudy{\'n}ski and Ekiel-Je{\.z}ewska.