Classical limit of the relativistic Vlasov-Maxwell-Landau system

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.