Mild solutions for the relativistic Vlasov-Maxwell system for laser-plasma interaction

We study a reduced 1D Vlasov-Maxwell system which describes the laser-plasma interaction. The unknowns of this system are the distribution function of charged particles, satisfying a Vlasov equation, the electrostatic field, verifying a Poisson equation and a vector potential term, solving a nonlinear wave equation. The nonlinearity in the wave equation is due to the coupling with the Vlasov equation through the charge density. We prove here the existence and uniqueness of the mild solution (i.e., solution by characteristics) in the relativistic case by using the iteration method.