On the relativistic BGK-Boltzmann model: asymptotics and hydrodynamics

TL;DR

This paper revisits the relativistic BGK-Boltzmann model, addressing key issues like parameter determination, various limits, entropy principles, and linearized operator analysis to deepen understanding of relativistic kinetic theory.

Contribution

It provides a comprehensive analysis of the relativistic BGK model, clarifying physical parameters and exploring classical, ultra-relativistic, and hydrodynamical limits.

Findings

Determination of physical parameters in the relativistic setting

Analysis of classical and ultra-relativistic limits

Insights into maximum entropy principles and linearized operator

Abstract

The generalization of the BGK relaxation model to the special relativity setting is revisited here. We deal with several issues related to this relativistic kinetic model which seem to have been overlooked in the previous physical literature, including the unique determination of associated physical parameters, classical, ultra-relativistic and hydrodynamical limits, maximum entropy principles and the analysis of the linearized operator.