The hard potential relativistic Boltzmann equation in the whole space

TL;DR

This paper investigates the relativistic Boltzmann equation with hard potentials in the entire space, establishing global solutions and optimal decay rates for initial data with finite supremum norm.

Contribution

It extends the analysis of the relativistic Boltzmann equation to hard potentials in the whole space, constructing global solutions and deriving decay rates.

Findings

Established existence of global mild solutions for initial data with finite $L^ abla$ norm.

Proved optimal time decay rates of solutions.

Handled the case of hard potentials in the relativistic setting.

Abstract

We study the Cauchy problem for the relativistic Boltzmann equation near relativistic Maxwellians in the whole space. The purpose of this article is to handle hard potentials, and for initial data with finite $L^\infty$ norm, to construct global in time mild solutions. We also prove the optimal time decay rates of the solutions.