On a kinetic equation describing the behavior of a gas interacting mainly with radiation

TL;DR

This paper investigates a kinetic model of gas-radiation interaction, analyzing the limiting behavior when gas-photon interactions dominate, and establishes well-posedness and convergence to a new kinetic equation.

Contribution

It introduces a new kinetic equation for gas-radiation systems and proves well-posedness and convergence in a specific scaling limit.

Findings

Proved well-posedness of the limit kinetic equation

Established convergence of solutions to the limit model

Analyzed dynamics near the slow manifold of steady states

Abstract

In this article we study a kinetic model which describes the interaction between a gas and radiation. Specifically, we consider a scaling limit in which the interaction between the gas and the photons takes place much faster than the collisions between the gas molecules themselves. We prove in the homogeneous case that the solutions of the limit problem solve a kinetic equation for which a well-posedness theory is considered. The proof of the convergence to a new kinetic equation is obtained analyzing the dynamics of the gas-photon system near the slow manifold of steady states.