Stabilities for Euler-Poisson Equations in Some Special Dimensions

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 $\gamma$.