From Vlasov-Maxwell-Landau system with Coulomb potential to two-fluid incompressible Navier-Stokes-Fourier-Maxwell system with Ohm's law

Abstract: In the diffusive regime, we obtain the uniform in Knudsen number estimate on the two-species Vlasov-Maxwell-Landau system with Coulomb potential around the global equilibrium. As a consequence, we justify the limit to the two-fluid incompressible Navier-Stokes-Fourier-Maxwell (NSFM) system with Ohm's law. This is the first result on the global in time uniform in Knudsen number estimate on the Boltzmann and Landau type equations with Coulomb potential coupled Vlasov-Maxwell equations.