Global strong solution and diffusive limit of the two-species Vlasov–Poisson–Boltzmann system

In this paper, we investigate global strong solution and diffusive limit of the two-species Vlasov–Poisson–Boltzmann system in R3 for the full range of cutoff hard potentials 0 ≤ γ ≤ 1. By introducing a new Hx,v2−Wx,v1,∞ framework, which is based on the interplay between the velocity weighted Hx,v2 energy estimate and the time-velocity weighted Wx,v1,∞-estimate for the two-species Vlasov–Poisson–Boltzmann system, we construct the global weighted estimate uniformly in the Knudsen number ɛ ∈ (0, 1]. As a result, global strong solution is constructed and the two-fluid incompressible Navier–Stokes–Fourier–Poisson limit is rigorously justified for all cutoff hard potentials 0 ≤ γ ≤ 1.