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

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

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Michael Kunzinger, Gerhard Rein, Roland Steinbauer, Gerald Teschl. 2002-09-25. Global Weak Solutions of the Relativistic Vlasov-Klein-Gordon System. https://doi.org/10.1007/s00220-003-0861-1

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