THE RELATIVISTIC VLASOV-MAXWELL-BOLTZMANN SYSTEM FOR SHORT RANGE INTERACTION

We are concerned with the Cauchy problem of the relativistic Vlasov-Maxwell-Boltzmann system for short range interaction. 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. Our proof is based on a new time-velocity weighted energy method and some optimal temporal decay estimates on the solution itself. The results also extend the case of "hard ball" model considered by Guo and Strain [Comm. Math. Phys. 310: 49-673 (2012)] to the short range interactions.