Article

**Comm. Math. Phys. 238, 367-378 (2003)**[DOI: 10.1007/s00220-003-0861-1]

## Global Weak Solutions of the Relativistic Vlasov-Klein-Gordon System

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

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.

** MSC91:** Primary 35D05, 35Q72; Secondary 35Q40, 82C22

**Keywords:** *Vlasov equation, Klein-Gordon equation, global weak solutions*

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