From two species Vlasov-Maxwell-Boltzmann system to magnetohydrodynamics system

Abstract

In this work, the magnetohydrodynamics system is formally derived from two species Vlasov-Maxwell-Boltzmann system. By employing the hypocoercivity of the linear Boltzmann operator and overcoming the difficulties resulting from the singular Lorentz term, we first obtain the uniform estimates of solutions with respect to the Knudsen number and then derive the magnetohydrodynamics system from the dimensionless Valsov-Maxwell-Boltzmann system.