Figures of equilibrium of an inhomogeneous self-gravitating fluid

TL;DR

This paper investigates the equilibrium shapes of a rotating, inhomogeneous self-gravitating fluid with density stratification and steady velocity, extending classical models to include inhomogeneity and internal flow.

Contribution

It introduces a framework for analyzing equilibrium figures of inhomogeneous fluids with stratification and steady internal motion, advancing classical rotating fluid models.

Findings

Derived conditions for equilibrium shapes of stratified fluids.

Extended classical models to include inhomogeneity and steady velocity fields.

Provided mathematical descriptions of equilibrium figures with density stratification.

Abstract

This paper is concerned with the figures of equilibrium of a self-gravitating ideal fluid with density stratification and a steady-state velocity field. As in the classical setting, it is assumed that the figures or their layers uniformly rotate about an axis fixed in space.