Stabilities for Euler–Poisson equations in some special dimensions

• Published in: Journal of mathematical analysis and applications Vol. 344; no. 1; pp. 145 - 156
• Main Author: Yuen, Manwai
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01-08-2008; Elsevier
• Subjects: Euler–Poisson equations; Exact sciences and technology; Mathematical analysis; Mathematics; Partial differential equations; Sciences and techniques of general use; Second inertia; Stability; Second inertia; Euler–Poisson equations; Stability; Damping; Euler equation; Mathematical analysis; Existence of solution; Euler-Poisson equations; Poisson equation; Application; Numerical stability; Non existence
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2008.02.025

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
|
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|
2
+
2
P
)
d
x
<
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M
2
−
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, for any
γ.