Optimal time decay of the Boltzmann system for gas mixtures

In this paper, we are concerned with the Boltzmann equation for the mixture of vapors of two gases in the whole space. Given the initial data of one gas near vacuum and the other near a global Maxwellian state, we obtain the global existence and optimal large time behaviors of the Boltzmann system for such binary mixture. The proof is based on Kawashima’s compensating function technique and a refined energy method.