Global Weak Solutions of the Relativistic Vlasov-Klein-Gordon System
  We consider an ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, which we call the relativistic Vlasov-Klein-Gordon system, we prove the existence of global weak solutions for initial data satisfying a size restriction. The latter becomes necessary since the energy of the system is indefinite, and only for restricted data a-priori bounds on the solutions can be derived from conservation of energy. 
Michael Kunzinger, Gerhard Rein, Roland Steinbauer, Gerald Teschl