Global classical solutions to the spherically symmetric Nordström-Vlasov system

Abstract

Classical solutions of the spherically symmetric Nordström-Vlasov system are shown to exist globally in time. The main motivation for investigating the mathematical properties of the Nordström-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 Nordström-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.

8 pages, LaTeX

References in corpus (4)

• Theorems on existence and global dynamics for the Einstein equations
• Spherically symmetric steady states of galactic dynamics in scalar gravity
• Global weak solutions to the Nordström-Vlasov system
• On classical solutions of the Nordström-Vlasov system

Cited by in corpus (5)

• Theorems on existence and global dynamics for the Einstein equations
• Global classical solutions to the 3D Nordström-Vlasov system
• Multipole radiation in a collisonless gas coupled to electromagnetism or scalar gravitation
• On global existence for the spherically symmetric Einstein-Vlasov system in Schwarzschild coordinates
• Cosmology and gravitational waves in the Nordstrom-Vlasov system, a laboratory for Dark Energy