Global existence and time decay estimates of the Vlasov-Boltzmann system

In this paper, we combine the method of constructing the compensating function and the energy method for the study on the Vlasov-Boltzmann system, which describes the evolution of the fluid of two species of particles interacting through the strong short range and weak long range pair potentials. Both the global existence and the optimal convergence rates of the solution around the global Maxwellians are obtained. The method used here has its own advantage, i.e., it does not involve the spectrum analysis of the corresponding linearized operator.