Stability of the Vlasov–Poisson–Boltzmann system in

We construct global-in-time classical solutions to the Cauchy problem for the 2-species Vlasov–Poisson–Boltzmann system near Maxwellian in the whole space . Moreover, the convergence rate in time to the global Maxwellian, and the uniform-in-time stability of solutions are also obtained through energy method.