Self-gravitating Newtonian disks revisited

TL;DR

This paper revisits stationary, self-gravitating Newtonian fluid disks, establishing new theorems on their extent and mass bounds, extending previous static results to rotating configurations.

Contribution

It introduces a theorem preventing infinite extension of fluids based on the equation of state and rotation law, and provides a Sobolev bound and Jeans-type inequality for stationary fluids.

Findings

Infinite extension of fluids is forbidden under certain conditions.

A Sobolev bound on the fluid mass is established.

A Jeans-type inequality for stationary fluids is derived.

Abstract

Recent analytic results concerning stationary, self-gravitating fluids in Newtonian theory are discussed. We give a theorem that forbids infinitely extended fluids, depending on the assumed equation of state and the rotation law. This part extends previous results that have been obtained for static configurations. The second part discusses a Sobolev bound on the mass of the fluid and a rigorous Jeans-type inequality that is valid in the stationary case.