| 郭俐辉,盛万成.Chaplygin气体Euler方程组的轴对称解[J].数学年刊A辑,2011,32(2):193~204 |
| Chaplygin气体Euler方程组的轴对称解 |
| Axisymmetric Solutions of the Euler System for the Chaplygin Gas |
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| DOI： |
| 中文关键词: Chaplygin气体的Euler方程组 完全线性退化 轴对称解 |
| 英文关键词:Euler system for the Chaplygin gas Fully linear degenerate Axisymmetric solutions |
| 基金项目:国家自然科学基金(No.10971130); 上海市重点学科建设基金(No.J50101); 上海市教委创新基金重点项目(No.11ZZ84); 新疆维吾尔自治区高校科研计划(No.XJEDU2009S11)资助的项目 |
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| 中文摘要: |
| 构造了两维Chaplygin气体Euler方程组的三参数、自相似的弱解. 在自相似和轴对称的假设下, 两维Chaplygin气体Euler方程组可以化为无穷远边值的常微分方程组,
由此得到了解的存在性和解的结构. 与多方气体不同的是Chaplygin气体的Euler方程组是完全线性退化的. 即使在轴向速度大于零的时候解也会出现间断现象.
这些解展示了宇宙演化过程中的一些现象, 例如黑洞的形成与演化以及宇宙的暴涨和膨胀. |
| 英文摘要: |
| In this paper, a three-parameter family of self-similar weak solutions are constructed in two-dimensional
space for all positive time
to the axisymmetric Euler equations for the Chaplygin gas. Under the self-similar and axisymmetry assumptions, the equations are
reduced to a system of three ordinary differential equations with boundary value at infinity, from which the detailed structures of
solutions as well as their existence are obtained. Different from polytropic gas, the Euler equations for the Chaplygin gas is
fully linear degenerate. Discontinuities exist even though the velocity of radially direction is positive. These solutions
exhibit some phenomena, such as black hole, expansion and explosive expansion, in the evolution of universe. |
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