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

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.

arXiv comment43 pages

References in corpus (4)

• The Incompressible Navier-Stokes Limit of the Boltzmann Equation for Hard Cutoff Potentials
• Cooling process for inelastic Boltzmann equations for hard spheres, Part I: The Cauchy problem
• On existence and uniqueness to homogeneous Boltzmann flows of monatomic gas mixtures
• LTE and Non-LTE Solutions in Gases Interacting with Radiation

Cited by in corpus (3)

• On the diffusion approximation of the stationary radiative transfer equation with absorption and emission
• Equilibrium and Non-Equilibrium diffusion approximation for the radiative transfer equation
• Quantitative pointwise estimates of the cooling process for inelastic Boltzmann equation