Note on the descriptions of the Euler-Poisson equations in various co-ordinate systems

TL;DR

This paper provides rigorous mathematical derivations of the Euler-Poisson equations in various coordinate systems, aiding future mathematical research despite not presenting new astrophysical results.

Contribution

It offers detailed, mathematically rigorous derivations of the Euler-Poisson equations in different coordinate systems, filling a gap in existing literature.

Findings

Rigorous derivations of Euler-Poisson equations in multiple coordinate systems

Clarification of mathematical foundations for astrophysical models

Preparation for advanced mathematical analysis of gaseous star dynamics

Abstract

In this note we derive the descriptions of the system of Euler-Poisson equations which governs the hydrodynamic evolution of gaseous stars in various co-ordinate systems. This note does not contain essentially new results for astrophysicists, but mathematically rigorous derivations cannot be found in the literatures written by physicists so that it will be useful to prepare details of rather stupidly honest derivations of the equations in various flames when we are going to push forward the mathematical research of the problem.