On the Vlasov-Poisson-Boltzmann limit of the Vlasov-Maxwell-Boltzmann system

TL;DR

This paper rigorously justifies the limit transition from the Vlasov-Maxwell-Boltzmann system to the Vlasov-Poisson-Boltzmann system as the light speed tends to infinity, ensuring the result holds globally in time.

Contribution

It provides a rigorous mathematical proof of the limit from Vlasov-Maxwell-Boltzmann to Vlasov-Poisson-Boltzmann systems for all cutoff interactions, including uniform a priori estimates.

Findings

The limit holds globally in time in a perturbative framework.

The analysis handles degeneracy of electromagnetic dissipation at large light speed.

The proof covers the entire range of cutoff intermolecular interactions.

Abstract

For the whole range of cutoff intermolecular interactions, we give a rigorous mathematical justification of the limit from the Vlasov-Maxwell-Boltzmann system to the Vlasov-Poisson-Boltzmann system as the light speed tends to infinity.Such a limit is shown to hold global-in-time in the perturbative framework.The key point in our analysis is to deduce certain a priori estimates which are independent of the light speed and the main difficulty is due to the degeneracy of the dissipative effect of the electromagnetic field for large light speed.