Global Solution of an Initial-Value Problem for Two-Dimensional Compressible Euler Equations
Global Solution of an Initial-Value Problem for Two-Dimensional Compressible Euler Equations
复制标题
DOI：
10.1006/jdeq.2001.4025
复制
发表时间：
2002-02
影响因子：
2.4
通讯作者：
Jiequan Li
中科院分区：
文献类型：
--
作者：
Jiequan Li
摘要本文讨论了可压缩欧拉方程楔形气体向真空中膨胀的整体连续解的存在性。通过速度图变换，我们首先证明了流动是由一个二阶偏微分方程组控制的，在无旋性条件下，这个偏微分方程组在相空间中被化为两个非齐次线性退化方程组。然后将这一结论应用于解决楔形气体膨胀为真空的问题，这实际上是超音速区域内这两个方程的Goursat类问题。
Abstract This paper is concerned with the existence of global continuous solutions of the expansion of a wedge of gas into a vacuum for compressible Euler equations. By hodograph transformation, we first prove that the flow is governed by a partial differential equation of second order, which is further reduced to a system of two nonhomogeneous linearly degenerate equations in the phase space under an irrotationality condition. Then this conclusion is applied to solving the problem that a wedge of gas expands into a vacuum, which is actually a Goursat-type problem for these two equations in the supersonic domain.