Inhomogeneous relativistic Boltzmann equation near vacuum in the Robertson-Walker space-time

TL;DR

This paper studies the relativistic Boltzmann equation in Robertson-Walker space-time with near vacuum initial data, establishing the existence of a unique global mild solution for hard potentials.

Contribution

It provides the first global existence result for the relativistic Boltzmann equation near vacuum in an expanding universe setting.

Findings

Existence of a unique global mild solution

Solution applies to hard potential collision kernels

Analysis conducted in a weighted function space

Abstract

In this paper, we consider the Cauchy problem for the relativistic Boltzmann equation with near vacuum initial data where the distribution function depends on the time, the position and the impulsion. The collision kernel considered here is for the hard potentials case and the background space-time in which the study is done is the Robertson-Walker space-time. Unique global (in time) mild solution is obtained in a suitable weighted space.