Scattering map for the Vlasov-Maxwell system around source-free electromagnetic fields

Abstract

We construct an isometric modified scattering operator, mapping any sufficiently regular past scattering state, with a small distribution function, to the future one corresponding to forward evolution by the Vlasov-Maxwell system. The main part of this work is devoted to the construction of a modified wave operator, which relates the future asymptotic dynamics of the solutions to their initial data. Then, by applying our previous results on modified scattering, we are able to construct a small data scattering map for the Vlasov-Maxwell system. Our analysis relies in particular on the study of the asymptotic Maxwell equations. Its solution captures not only the large time behavior of the electromagnetic field of the plasma near future timelike infinity as well as future null infinity, but also the one of its weighted derivatives. The wave operator provides as well a class of global solutions to the Vlasov-Maxwell system which are large in $L^p_{x,v}\times L^2_x$ but initially dispersed.