Stability of the relativistic Vlasov–Maxwell–Boltzmann system for short range interaction

The Cauchy problem of the relativistic Vlasov–Maxwell–Boltzmann system for short range interaction is investigated. For perturbative initial data with suitable regularity and integrability, we prove the large time stability of solutions to the relativistic Vlasov–Maxwell–Boltzmann system, and also obtain as a byproduct the convergence rates of solutions. For the proof, a new interactive instant energy functional is introduced to capture the the macroscopic dissipation and the very weak electro-magnetic dissipation of the linearized system. A refined time–velocity weighted energy method is also applied to compensate the weaker dissipation of the linearized collision operator in the case of non-hard potential models. The results also extend the case of “hard ball” model considered by Guo and Strain (2012) to the short range interactions.