Global weak solutions to the Nordstr\"om-Vlasov system

TL;DR

This paper proves the existence of global weak solutions for the Nordström-Vlasov system, a model for self-gravitating collisionless gases, by establishing a-priori bounds and improving continuation criteria.

Contribution

It introduces new a-priori bounds and extends the continuation criterion, enabling the proof of global weak solutions for the system.

Findings

Existence of global weak solutions established.

Weak solutions preserve mass.

Improved continuation criterion for classical solutions.

Abstract

The Nordstr\"om-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.