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

Michael Kunzinger·Gerhard Rein·Roland Steinbauer·Gerald Teschl
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Abstract

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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Michael Kunzinger, Gerhard Rein, Roland Steinbauer, Gerald Teschl. 2004-07-02. On Classical Solutions of the Relativistic Vlasov-Klein-Gordon System. https://arxiv.org/abs/math/0407028

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