Existence of Global Solution of the Cauchy Problem for the Relativistic Boltzmann Equation with Hard Interactions

TL;DR

This paper proves the existence of a global mild solution to the relativistic Boltzmann equation with hard interactions, extending techniques from the nonrelativistic case to the relativistic setting under certain physical assumptions.

Contribution

It establishes the existence of global solutions for the relativistic Boltzmann equation using DiPerna and Lions techniques, considering relativistic scattering and initial data with finite physical quantities.

Findings

Global mild solution exists for the relativistic Boltzmann equation

Results include cases with relativistic hard interactions

Initial data with finite mass, inertia, energy, and entropy suffices

Abstract

By using the DiPerna and Lions techniques for the nonrelativistic Boltzmann equation, it is shown that there exists a global mild solution to the Cauchy problem for the relativistic Boltzmann equation with the assumptions of the relativistic scattering cross section including some relativistic hard interactions and the initial data satifying finite mass, ``inertia'', energy and entropy.