Global Solution to the Relativistic Enskog Equation With Near-Vacuum Data

TL;DR

This paper proves the existence and uniqueness of global solutions to the relativistic Enskog equation for a hard sphere gas near vacuum, based on two hypotheses about the collision kernel.

Contribution

It introduces two hypotheses for the relativistic collision kernel and establishes global existence and uniqueness results for solutions near vacuum.

Findings

Existence and uniqueness of solutions near vacuum

Validation of hypotheses for the collision kernel

Mathematical framework for relativistic kinetic equations

Abstract

We give two hypotheses of the relativistic collision kernal and show the existence and uniqueness of the global mild solution to the relativistic Enskog equation with the initial data near the vacuum for a hard sphere gas.