Properties of weak solutions to the Nordström–Vlasov system

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.