On Classical Solutions of the Relativistic Vlasov-Klein-Gordon System
  We consider a collisionless ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential 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. 
Michael Kunzinger, Gerhard Rein, Roland Steinbauer, Gerald Teschl