On Classical Solutions of the Relativistic Vlasov-Klein-Gordon System

Details On Classical Solutions of the Relativistic Vlasov-Klein-Gordon System On Classical Solutions of the Relativistic Vlasov-Klein-Gordon System

2004-07-02

arxiv.org/abs/math/0407028v1

Electron. J. Differential Equations 2005, no. 01, 17 pp.

Mathematics

Analysis of PDEs

18 pages, LaTeX

Scientific paper

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.

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