Dispersive behavior in Galactic Dynamics

TL;DR

This paper investigates dispersive solutions in galactic dynamics, establishing conditions for their existence and providing examples, thereby advancing understanding of gravitational Vlasov-Poisson systems.

Contribution

It introduces necessary and sufficient conditions for dispersive solutions in the gravitational Vlasov-Poisson system, including inequalities involving energy, mass, and momentum.

Findings

Derived inequalities for dispersive solutions

Identified conditions for statistical dispersion

Analyzed examples like steady and virialized states

Abstract

The purpose of this paper is to study the relations between different concepts of dispersive solution for the Vlasov-Poisson system in the gravitational case. Moreover we give necessary conditions for the existence of partially and totally dispersive solutions and a sufficient condition for the occurence of statistical dispersion. These conditions take the form of inequalities involving the energy, the mass and the momentum of the solution. Examples of dispersive and non-dispersive solutions--steady states, periodic solutions and virialized solutions--are also considered.