Global Hilbert expansion for the relativistic Vlasov-Maxwell-Boltzmann system

Abstract

Consider the relativistic Vlasov-Maxwell-Boltzmann system describing the dynamics of an electron gas in the presence of a fixed ion background. Thanks to recent works \cite{Germain-Masmoudi-ASENS-2014, Guo-Ionescu-Pausader-JMP-2014} and \cite{Deng-Ionescu-Pausader-ARMA-2017}, we establish the global-in-time validity of its Hilbert expansion and derive the limiting relativistic Euler-Maxwell system as the mean free path goes to zero. Our method is based on the $L^2-L^{\infty }$ framework and the Glassey-Strauss Representation of the electromagnetic field, with auxiliary $H^1$ estimate and $W^{1,\infty }$ estimates to control the characteristic curves and corresponding $L^{\infty }$ norm.

This new version contains correction of errors and typos for published paper (Commun. Math. Phys. 384(1): 341-401,2021)

References in corpus (2)

• Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials
• Hilbert Expansion from the Boltzmann equation to relativistic Fluids

Cited by in corpus (1)

• An introduction to the relativistic kinetic theory on curved spacetimes