LTE and Non-LTE Solutions in Gases Interacting with Radiation

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.