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A Boltzmann equation, used to describe the evolution of the density functionof a gas of photons interacting by Compton scattering with electrons at lowdensity and non relativistic equilibrium, is considered. A truncation of thevery singular redistribution function is introduced and justified. Theexistence of weak solutions is proved for a large set of initial data. Asimplified equation, where only the quadratic terms are kept and that appearsat very low temperature of the electron gas, for small values of the photon'senergies, is also studied. The existence of weak solutions, and also of moreregular solutions that are very flat near the origin, is proved. The long timeasymptotic behavior of weak solutions of the simplified equation is described.

On a Boltzmann equation for Compton scattering, from non relativistic electrons at low density