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 $\gamma >\max \{-3,-\frac{3}{2}-2s\}$, including both strong angular singularity $\frac{1}{2}\le s<1$ and weak angular singularity $0<s<\frac{1}{2}$. Uniform estimate with respect to the Knudsen number $\epsilon \in (0,1]$ 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 $\gamma >\max \{-3,-\frac{3}{2}-2s\}$ 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.