论文标题
在对称下的分层公理对称Euler-Poisson方程的降低
Reduction of Stratified Axi-Symmetric Euler-Poisson Equations Under Symmetry
论文作者
论文摘要
本文认为在额外的假设是不可压缩的和分层的，它考虑了自我吸引，旋转，旋转的对称流体的稳态的Euler-Poisson方程。在这种情况下，我们表明，六个非线性偏微分方程的原始系统可以简化为两个方程，一个用于质量密度，另一个用于重力场。这种还原是在圆柱坐标中进行的。结果，我们能够得出压力作为密度函数的表达式。然后通过分析求解所得的方程。然后，使用这些分析溶液来确定旋转星（或星际云）的形状，通过应用边界条件在边界处的压力为零。
The paper considers Euler-Poisson equations which govern the steady state of a self gravitating, rotating, axi-symmetric fluid under the additional assumption that it is incompressible and stratified. In this setting we show that the original system of six nonlinear partial differential equations can be reduced to two equations, one for the mass density and the other for gravitational field. This reduction is carried out in cylindrical coordinates. As a result we are able to derive also expressions for the pressure as a function of the density. The resulting equations are then solved analytically. These analytic solutions are used then to determine the shape of the rotating star (or interstellar cloud) by applying the boundary condition that the pressure is zero at the boundary.
