欧拉泊松方程平衡解的稳定性  

The Stability for Stationary Solution of Euler-Poisson Equations

作　　者：谢华朝[1] 李素丽[1] 

机构地区：[1]河南财经政法大学数学与信息科学学院,郑州450046

出　　处：《应用数学学报》2015年第4期619-631,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11326136;61203050);河南省教育厅(14B110033;15A110010)资助项目

摘　　要：三维空间中,欧拉泊松方程描述可压等熵理想气态星体的运动.本文研究气态星体平衡解的存在性及其非线性稳定性.证明了在1/(γ-1)∫_(R^3)ρ~γdx=M不变和确定的旋转速度下,当绝热指数6/5<γ<2时,方程对应的能量泛函的极小化子存在,且该极小化子是欧拉泊松方程的平衡解;进而证明平衡解是非线性稳定的.如果星体速度为零,密度的紧支集是球,那么欧拉泊松方程的平衡解是径向唯一的.In three dimension space, the motion of a compressible isentropic perfect gaseous stars with self-gravitation is modeled by the Euler-Poisson equations. The main purpose of this paper is concerned with stationary solutions and the nonlinear stability of gaseous stars. Under a case that 1/（γ-1）∫R3ρ~γdx=M is conserved, with prescribed angular velocity, if 6/5〈γ〈2, we prove the existence of stationary solution of E-P equations; the nonlinear stability of such steady states is also proved. If v v≡ 0, the support of ρ is BR（0）, then the stationary solution of E-P equations is spherically symmetric and unique.

关 键 词：气态星体 欧拉泊松方程 平衡解 非线性稳定性 

分 类 号：O175.2[理学—数学]