Existence of axially symmetric solutions to the Vlasov-Poisson system depending on Jacobi's integral

TL;DR

This paper proves the existence of axially symmetric steady-state solutions to the Vlasov-Poisson system in a rotating frame, depending on Jacobi's integral, using an implicit function theorem for operators.

Contribution

It establishes the existence of such solutions under small angular velocities, extending the understanding of rotating stellar systems.

Findings

Existence of axially symmetric solutions for small angular velocities

Solutions depend on Jacobi's integral

Method relies on an implicit function theorem

Abstract

We prove the existence of axially symmetric solutions to the Vlasov--Poisson system in a rotating setting for sufficiently small angular velocity. The constructed steady states depend on Jacobi's integral and the proof relies on an implicit function theorem for operators.