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

TL;DR

This paper establishes uniform estimates for the Vlasov-Maxwell-Landau system with Coulomb potential in the diffusive regime and rigorously derives the two-fluid incompressible NSFM system with Ohm's law as a limit.

Contribution

It provides the first global-in-time uniform in Knudsen number estimate for Coulomb potential coupled Vlasov-Maxwell-Landau equations and justifies the hydrodynamic limit to the NSFM system.

Findings

Uniform in Knudsen number estimate established

Rigorous derivation of the two-fluid NSFM system from kinetic equations

First such result for Coulomb potential coupled Vlasov-Maxwell equations

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.