CONTROLLING THE PROPAGATION OF THE SUPPORT FOR THE RELATIVISTIC VLASOV EQUATION WITH A SELFCONSISTENT LORENTZ INVARIANT FIELD

Successful techniques have been developed for controlling the propagat ion of the support (preventing blow up) for the classical Vlasov-Poiss on equation, leading to global existence of smooth solutions. It is we ll known that these techniques all fail for the relativistic Vlasov-Po isson equation. This equation is a hybrid of a relativistic transport equation and a classical, Galilean invariant, field equation. In this paper we introduce a new equation for the field making it Lorentz inva riant. We show that the propagation of the support, for solutions sati sfying this equation and the relativistic Vlasov equation, may be cont rolled.