Classical limit of the relativistic Vlasov-Maxwell-Landau system

TL;DR

This paper rigorously justifies the non-relativistic limit of the relativistic Vlasov-Maxwell-Landau system to the Vlasov-Poisson-Landau system as the speed of light approaches infinity, using advanced mathematical techniques.

Contribution

It introduces new coercivity estimates, a weighted energy functional, and proves global well-posedness to rigorously justify the non-relativistic limit.

Findings

Established uniform coercivity estimate for relativistic Landau operator

Constructed a novel weighted energy functional

Proved global well-posedness in the non-relativistic limit

Abstract

The physical essence of the non-relativistic limit, from the relativistic Vlasov-Maxwell-Landau system to the Vlasov-Poisson-Landau system, lies in the transition from finite-speed electromagnetic waves to instantaneous Coulomb interactions, and from relativistic to Newtonian particle dynamics. We rigorously justify this limit (mathematically corresponding to the light speed $c \to \infty$) in a periodic box via three key technical advances: establishing a uniform-in-$c$ coercivity estimate for the relativistic Landau collision operator, constructing a novel weighted energy functional to overcome the weakening dissipation of the electromagnetic field at large $c$, and proving a corresponding global well-posedness result.