Properties of weak solutions to the Nordström–Vlasov system

Abstract

In this article, we investigate the Nordström–Vlasov system in the whole space. The kinetic model is a relativistic generalization of the classical Vlasov–Poisson system in the gravitational case and describes the ensemble motion of collisionless particles interacting by means of a self-consistent scalar gravitational field. With the Fourier analysis and the smoothing effect of low velocity particles, we get a better regularity of weak solutions for the field than the one proved by Calogero and Rein [J. Differ. Equ. 204, 323 (2004)]. Meanwhile, under the additional integrability condition, we establish the energy conservation of the weak solution.