On classical solutions of the relativistic Vlasov-Klein-Gordon system.

We consider a collisionless ensemble of classical particles coupled with a Klein-Gordon field. For the resulting nonlinear system of partial dier- ential equations, the relativistic Vlasov-Klein-Gordon system, we prove local- in-time existence of classical solutions and a continuation criterion which says that a solution can blow up only if the particle momenta become large. We also show that classical solutions are global in time in the one-dimensional case.