中山大学学报自然科学版 ›› 2017, Vol. 56 ›› Issue (1): 74-76.

• 研究论文 • 上一篇    下一篇

欧拉-泊松方程组的自相似解

王玲1,夏莉2   

  1. 1. 广东水利电力职业技术学院数学部,广东 广州 510635;
    2. 广东财经大学数学与统计学院,广东 广州 510320
  • 收稿日期:2016-06-21 出版日期:2017-01-25 发布日期:2017-01-25
  • 通讯作者: 王玲(1966年生),女;研究方向:数学教育、偏微分方程;Email: wanglin@gdsdxy.cn

Self-similar solutions for the compressible Euler-Poisson equations in three dimension

WANG Ling1, XIA Li2   

  1. 1. Department of Mathematics, Guangdong Technical College of Water Resources and Electric Engineering, Guangzhou 510635, China;
    2. College of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou 510320, China
  • Received:2016-06-21 Online:2017-01-25 Published:2017-01-25

摘要:

三维可压等熵欧拉泊松方程组描述可压等熵理想气态星体的运动规律,它由质量守恒方程、动量守恒方程及自引力位势满足的泊松方程构成。研究欧拉泊松方程组的自相似解是天体物理及数学领域研究的热点问题之一,具有重要的现实意义和广阔的应用前景。关于三维可压等熵欧拉泊松方程组自相似解的研究较少。用分离变量法研究了一类三维可压等熵欧拉泊松方程组的一组自相似解。

关键词: 三维可压等熵, 欧拉泊松方程组, 自相似解

Abstract:

The isentropic compressible Euler-Poisson equations, addressed to describe the motion of ideal gaseous stars, consist of the Euler-Poisson equations for the conservation of mass and momentum, and Poisson equation induced by the potential function of the self-gravitational force. Using the separation method, self-similar solution are presented for the isentropic compressible Euler-Poisson equations in three dimension.

Key words: isentropic compressible, Euler-Poisson equations, self-similar solutions, three dimension

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