The diffusive limits of two species Vlasov-Maxwell-Boltzmann equations

TL;DR

This paper rigorously analyzes the diffusive limits of the two species Vlasov-Maxwell-Boltzmann system, demonstrating how electromagnetic fields behave as the Knudsen number approaches zero, and deriving related fluid dynamic limits.

Contribution

It provides a rigorous justification for the Navier-Stokes, Navier-Stokes-Poisson, and Navier-Stokes-Maxwell limits of the system in three dimensions on the torus.

Findings

Electric and magnetic fields may persist or vanish in the diffusive limit.

Unified estimates of solutions are established using hypocoercivity techniques.

The study confirms the validity of fluid dynamic limits for the system.

Abstract

In this work, we mainly concern the limiting behavior of the electromagnetic field of two species Vlasov-Maxwell-Botlzmann system in diffusive limits. As knudsen numbers goes to zero, the electric magnetic and magnetic field may perserve or vanish. We verify rigorously Navier-Stokes, Navier-Stokes-Poisson and Navier-Stokes Maxwell limit of the two species Vlasov-Maxwell-Boltzmann system on the torus in three dimension. The justification is based on the unified and uniform estimates of solutions to the dimensionless Vlasov-Maxwell-Boltzmann. The uniform estimates of solutions are obtained by employing the hypocoercivity of the linear Boltzmann operator and constructing a equation containing damping term of electric field.