Stabilities for Euler-Poisson Equations in Some Special Dimensions

TL;DR

This paper investigates the stability and classical solutions of Euler-Poisson equations in specific dimensions, extending previous studies to include cases with or without damping and analyzing solution existence in 2D.

Contribution

It extends stability analysis of Euler-Poisson equations to special dimensions and proves non-global existence of solutions in 2D using the second inertia function.

Findings

Extended stability analysis to special dimensions with/without damping

Proved non-global existence of classical solutions in 2D

Used second inertia function to establish solution bounds

Abstract

We study the stabilities and classical solutions of Euler-Poisson equations of describing the evolution of the gaseous star in astrophysics. In fact, we extend the study the stabilities of Euler-Poisson equations with or without frictional damping term to some special dimensional spaces. Besides, by using the second inertia function in 2 dimension of Euler-Poisson equations, we prove the non-global existence of classical solutions with $2\int_{\Omega}(\rho| u| ^{2}+2P)dx<gM^{2}-\epsilon$, for any $\gamma$.