Relativistic Kinetic Theory of Polyatomic Gases: Classical Limit of a New Hierarchy of Moments and Qualitative Analysis

TL;DR

This paper develops a relativistic kinetic theory for polyatomic gases, introduces a new hierarchy of moments accounting for internal energy, and analyzes the classical limit and stability of a fifteen-moment closure system.

Contribution

It presents a novel hierarchy of moments for relativistic polyatomic gases and proves the classical limit and global existence of solutions for a fifteen-moment model.

Findings

Classical limit of the relativistic hierarchy matches classical kinetic theory.

The fifteen-moment system is symmetric hyperbolic and globally well-posed near equilibrium.

The new hierarchy accurately incorporates internal energy effects in relativistic gases.

Abstract

A relativistic version of the Kinetic Theory for polyatomic gas is considered and a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal modes is presented. In the first part, we prove via classical limit that the truncated system of moments dictates a precise hierarchy of moments in the classical framework. In the second part, we consider the particular physical case of fifteen moments closed via Maximum Entropy Principle in a neighborhood of equilibrium state. We prove that this symmetric hyperbolic system satisfies all the general assumption of some theorems that guarantee the global existence of smooth solutions for initial data sufficiently small.