Diffusive Limit of the Vlasov-Maxwell-Boltzmann System without Angular Cutoff

Diffusive limit of the non-cutoff Vlasov-Maxwell-Boltzmann system in perturbation framework still remains open. By employing a new weight function and making full use of the anisotropic dissipation property of the non-cutoff linearized Boltzmann operator, we solve this problem with some novel treatments for non-cutoff potentials γ > max\-3, -3/2-2s\, including both strong angular singularity 1/2 ≤ s <1 and weak angular singularity 0 < s < 1/2. Uniform estimate with respect to the Knudsen number ε∈ (0,1] is established globally in time, which eventually leads to the global existence of solutions to the non-cutoff Vlasov-Maxwell-Boltzmann system as well as hydrodynamic limit to the two-fluid incompressible Navier-Stokes-Fourier-Maxwell system with Ohm's law. The indicators γ > max\-3, -3/2-2s\ and $0 < s <1$ in this paper cover all ranges that can be achieved by the previously established global solutions to the non-cutoff Vlasov-Maxwell-Boltzmann system in perturbation framework.