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Global weak solutions to the Nordström-Vlasov system. (English) Zbl 1060.35027
Summary: The Nordström–Vlasov system is a Lorentz invariant model for a self-gravitating collisionless gas. We establish suitable a priori bounds on the solutions of this system, which together with energy estimates and the smoothing effect of ”momentum averaging” yield the existence of global weak solutions to the corresponding initial value problem. In the process we improve the continuation criterion for classical solutions which was derived recently. The weak solutions are shown to preserve mass.

MSC:
35D05 Existence of generalized solutions of PDE (MSC2000)
35B60 Continuation and prolongation of solutions to PDEs
35Q75 PDEs in connection with relativity and gravitational theory
83C40 Gravitational energy and conservation laws; groups of motions
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
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