Finite speed propagation of the solutions for the relativistic Vlasov–Maxwell system

In this paper, we investigate the continuous dependence with respect to the initial data of the solutions for the 1D and 1.5D relativistic Vlasov–Maxwell system. More precisely, we prove that these solutions propagate with finite speed. We formulate our results in the framework of mild solutions, i.e., the particle densities are solutions by characteristics and the electro-magnetic fields are Lipschitz continuous functions.