LTE and Non-LTE Solutions in Gases Interacting with Radiation

TL;DR

This paper investigates kinetic equations for radiative transfer in gases, analyzing LTE and non-LTE regimes, deriving related models, and establishing existence or non-existence of stationary solutions in each case.

Contribution

It introduces and compares LTE and non-LTE models for gas-radiation interactions, providing new existence and non-existence results for stationary solutions.

Findings

Existence of stationary solutions in LTE case

Non-existence of stationary solutions in non-LTE case

Derivation of Euler-like systems from kinetic equations

Abstract

In this paper, we study a class of kinetic equations describing radiative transfer in gases which include also the interaction of the molecules of the gas with themselves. We discuss several scaling limits and introduce some Euler-like systems coupled with radiation as an aftermath of specific scaling limits. We consider scaling limits in which local thermodynamic equilibrium (LTE) holds, as well as situations in which this assumption fails (non-LTE). The structure of the equations describing the gas-radiation system is very different in the LTE and non-LTE cases. We prove the existence of stationary solutions with zero velocities to the resulting limit models in the LTE case. We also prove the non-existence of a stationary state with zero velocities in a non-LTE case.