Global classical solutions to the spherically symmetric Nordstr\"om-Vlasov system

TL;DR

This paper proves the global existence of classical solutions for the spherically symmetric Nordström-Vlasov system, a simplified model related to Einstein-Vlasov, under certain angular momentum conditions, for large initial data.

Contribution

It establishes the first global existence result for classical solutions of the spherically symmetric Nordström-Vlasov system with large initial data under angular momentum bounds.

Findings

Solutions exist globally in time for compactly supported initial data.

The result applies to arbitrarily large initial data satisfying the angular momentum condition.

The condition on angular momentum is not a smallness assumption.

Abstract

Classical solutions of the spherically symmetric Nordstr\"{o}m-Vlasov system are shown to exist globally in time. The main motivation for investigating the mathematical properties of the Nordstr\"{o}m-Vlasov system is its relation to the Einstein-Vlasov system. The former is not a physically correct model, but it is expected to capture some of the typical features of the latter, which constitutes a physically satisfactory, relativistic model but is mathematically much more complex. We show that classical solutions of the spherically symmetric Nordstr\"{o}m-Vlasov system exist globally in time for compactly supported initial data under the additional condition that there is a lower bound on the modulus of the angular momentum of the initial particle system. We emphasize that this is not a smallness condition and that our result holds for arbitrary large initial data satisfying this hypothesis.