Regularity of weak solutions for the relativistic Vlasov-Klein-Gordon system

This article is devoted to the study of the relativistic Vlasov-Klein-Gordon system in space dimension three. The dynamical model describes a collisionless ensemble of classical particles coupled with a Klein-Gordon field. By combining the Fourier method and smoothing effect of low velocity particles, we prove a higher regularity of the field, which is widely used for the study of Vlasov equation.