Abstract
We study the stabilities and classical solutions of Euler–Poisson equations describing the evolution of the gaseous star in astrophysics. In fact, we extend the study of 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 ∫ Ω ( ρ | u | 2 + 2 P ) d x < g M 2 − ϵ , for any γ.
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