Asymptotic behavior of small solutions to the Vlasov--Klein--Gordon system in high dimensions

Abstract

We study the asymptotic behavior of small solutions to the Vlasov--Klein--Gordon system in high dimensions. The standard argument of Glassey and Strauss \cite{GS87} for studying small solutions to the Vlasov--Maxwell system does not apply to the Vlasov--Klein--Gordon system due to the massiveness of the Klein--Gordon field. In this paper we use the vector field method and consider solutions in dimensions $n\ge 4$ with the hyperboloidal foliation of the Minkowski spacetime to obtain the asymptotic properties for the Vlasov--Klein--Gordon system.