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

TeX file (38k) or pdf file (217k)