Stationary solutions for the one-dimensional Nordström–Vlasov system

Abstract

The Nordström-Vlasov system describes the evolution of self-gravitating collisionless particles. We prove the existence of stationary solutions in one dimension. We show also the propagation of impulsion moments and perform an asymptotic analysis.(1+|p| 2 ) 1/2 denotes the relativistic velocity of a particle with 0921-7134/09/$17.00

Spectral properties of general advection operators and weighted translation semigroups

“…where the potential φ is a given smooth function, say φ ∈ W 2,∞ (0, 1), and the relativistic velocity v(p) corresponding to the impulsion p ∈ R is given by v(p) = p √ 1+p 2 . The study of the above equation (2.6) is related to the relativistic Nordström-Vlasov systems for plasma (see [12,11] and the references therein). We can then define a smooth vector field over Ω = (0, 1) × R by…”