Article

**Electron. J. Differential Equations 2005, No. 01, 1-17 (2005)**[url]

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

### Michael Kunzinger, Gerhard Rein, Roland Steinbauer, and Gerald Teschl

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.

** MSC2000:** 35A07, 35Q72, 35Q40, 82C22

**Keywords:** *Vlasov equation; Klein-Gordon equation; classical solutions*

Download