Moment Propagation of the Vlasov-Poisson System with a Radiation Term

Abstract

We investigate the dynamics of the Vlasov-Poisson system in the presence of radiation damping. A propagation result for velocity moments of order $k>3$ is established in (Kunze and Rendall in Ann. Henri Poincare 2:857–886, 2001). In this paper, we prove existence of global solutions propagating velocity and velocity-spatial moments of order $k>2$ and establish an explicit polynomially growing in time bound on the moments.