On the Vlasov-Maxwell-Boltzmann system near Maxwellians

For the whole range of cutoff intermolecular interactions, we give a rigorous mathematical justification of the limit from the Vlasov-Maxwell-Boltzmann system to the Vlasov-Poisson-Boltzmann system as the light speed tends to infinity. Such a limit is shown to hold global-in-time in the perturbative framework. The key point in our analysis is to deduce certain a priori estimates which are independent of the light speed and the main difficulty is due to the degeneracy of the dissipative effect of the electromagnetic field for large light speed.