The classical limit of the relativistic Vlasov-Maxwell system in two space dimensions

The motion of a collisionless plasma is modeled by the Vlasov-Maxwell system. Here the speed of light, c, appears as a parameter. First we study the existence of classical solutions of the relativistic Vlasov-Maxwell system with smooth initial data, on a time interval independent of c. Then we show that solutions of the relativistic Vlasov-Maxwell system converge pointwise to solutions of the non relativistic Vlasov-Poisson system as c tends to infinity, at the asymptotic rate of 1/c.