Diffusive Limit of the One-species Vlasov-Maxwell-Boltzmann System for Cutoff Hard Potentials

TL;DR

This paper proves the diffusive limit of the one-species Vlasov-Maxwell-Boltzmann system for cutoff hard potentials, establishing global solutions and hydrodynamic limits using novel energy methods.

Contribution

It introduces a new weighted energy approach to solve the diffusive limit problem for the one-species Vlasov-Maxwell-Boltzmann system, covering the full range of cutoff hard potentials.

Findings

Established uniform estimates globally in time.

Proved global existence of solutions.

Derived hydrodynamic limit to incompressible Navier-Stokes-Fourier-Maxwell system.

Abstract

Diffusive limit of the one-species Vlasov-Maxwell-Boltzmann system in perturbation framework still remains unsolved, due to the weaker time decay rate compared with the two-species Vlasov-Maxwell-Boltzmann system. By employing the weighted energy method with two newly introduced weight functions and some novel treatments, we solve this problem for the full range of cutoff hard potentials $0\leq \gamma \leq 1$. Uniform estimate with respect to the Knudsen number $\varepsilon\in (0,1]$ is established globally in time, which eventually leads to the global existence of solutions to the one-species Vlasov-Maxwell-Boltzmann system and hydrodynamic limit to the incompressible Navier-Stokes-Fourier-Maxwell system. To the best of our knowledge, this is the first result on diffusive limit of the one-species Vlasov-Maxwell-Boltzmann system in perturbation framework.