From Vlasov-Maxwell-Boltzmann system to two-fluid incompressible Navier-Stokes-Fourier-Maxwell system with Ohm’s law: convergence for classical solutions

For the two-species Vlasov-Maxwell-Boltzmann (VMB) system with scaling under which moments of fluctuations to global Maxwellians formally converge two-fluid incompressible Navier-Stokes-Fourier-Maxwell (NSFM) Ohm's law, we prove uniform estimates respect Knudsen number $\eps$ for fluctuations. As consequences, existence in time classical solutions VMB all $\eps \in (0,1]$ is established. Furthermore, convergence NSFM law rigorously justified. This limit was justified recent breakthrough Ars\'enio and Saint-Raymond \cite{Arsenio-SRM-2016} from renormalized dissipative viscous electro-magneto-hydrodynamics corresponding scaling. In this sense, our result gives a solution analogue \cite{Arsenio-SRM-2016}.