On classical solutions of the relativistic Vlasov-Klein-Gordon system
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We consider a collisionless ensemble of classical particles coupled with 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.
CitationKunzinger, M., Rein, G., Steinbauer, R., & Teschl, G. (2005). On classical solutions of the relativistic Vlasov-Klein-Gordon system. Electronic Journal of Differential Equations, 2005(01), pp. 1-17.
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