Existence and uniqueness of mild solutions for BGK models for gas mixtures of polyatomic molecules

TL;DR

This paper investigates two BGK models for gas mixtures of polyatomic molecules, proving their solutions exist uniquely and differ from ideal gas law predictions, enhancing understanding of such complex systems.

Contribution

It establishes existence and uniqueness of positive solutions for two specific BGK models of polyatomic gas mixtures, highlighting their deviation from ideal gas behavior.

Findings

Models satisfy a different equation of state than ideal gas law.

Existence and uniqueness of positive solutions are proven.

Models account for internal energy degrees of freedom.

Abstract

We consider two models for a two component gas mixture with translational and internal energy degrees of freedom described by a BGK approximation assuming that the number of particles of each species remains constant. The two species are allowed to have different degrees of freedom in internal energy and are modelled by a system of kinetic BGK equations featuring two interaction terms to account for momentum and energy transfer between the species. We consider two models in the literature and prove that the models satisfy a different equation of state than the ideal gas law. Moreover, we prove that for these models there exist a unique positive solution.