The Diffusive Limit of the Vlasov–Boltzmann System for Binary Fluids

We consider the Vlasov–Boltzmann system describing the evolution of the fluid of two species of particles interacting through strong short range and weak long range pair potentials. We establish the global validity of diffusive expansions for solutions around Maxwellian equilibrium to the rescaled system. We prove the uniform boundedness and time-decay estimate for the remainders via a unified nonlinear energy method.