Compactness of linearized Boltzmann operators for polyatomic gases

TL;DR

This paper reviews recent results on the compactness of linearized Boltzmann operators for polyatomic gases, discusses the mixture case, and examines the physical relevance of assumptions with a specific collision kernel.

Contribution

It provides a comprehensive review of existing kinetic models and recent compactness results, including an analysis of the mixture case and physical assumptions.

Findings

Recent compactness results for linearized Boltzmann operators

Extension to mixture cases of polyatomic gases

Discussion on physical relevance of assumptions with specific collision kernels

Abstract

In this article, we recall various existing kinetic models of non-reactive polyatomic gases. We also review the results, all recently obtained, about the compactness of the associated linearized Boltzmann operator, and briefly investigate the mixture case. Eventually, with a specific collision kernel, we present a discussion about the physical relevance of the assumptions used to obtain the compactness results.