Michael Kunzinger, Gerhard Rein, Roland Steinbauer, Gerald Teschl
Global Weak Solutions of the Relativistic Vlasov-Klein-Gordon System
The paper is published: Commun. Math. Phys. 238 (2003) 367-378

MSC:

35D05 Existence of generalized solutions

35Q72 Other equations from mechanics

35Q40 Equations from quantum mechanics

82C22 Interacting particle systems, See also {60K35}

Abstract: 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.
Keywords: Vlasov equation, Klein-Gordon equation, global weak solutions