Interaction of Four Rarefaction Waves in the Bi-Symmetric Class of the Two-Dimensional Euler Equations
Interaction of Four Rarefaction Waves in the Bi-Symmetric Class of the Two-Dimensional Euler Equations
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DOI：
10.1007/s00220-010-1019-6
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发表时间：
2010-02
影响因子：
2.4
通讯作者：
Jiequan Li;Yuxi Zheng
中科院分区：
文献类型：
--
作者：
Jiequan Li;Yuxi Zheng
多维非定常可压缩欧拉方程解的整体存在性和结构是一个有趣而重要的开放问题。本文在初始稀疏波较大的情况下，构造了二维空间欧拉方程中四个具有两对称轴的正交平面稀疏波相互作用的全局经典解。双对称初始数据是四波二维黎曼问题的一种基本类型。这种情况下的解是连续的、有界的和自相似的，并且我们描述了稀疏波必须有多大。我们使用了相位变换、特征分解和相空间分析的方法。在此过程中，我们解决了简单波的二元相互作用。
The global existence and structures of solutions to multi-dimensional unsteady compressible Euler equations are interesting and important open problems. In this paper, we construct global classical solutions to the interaction of four orthogonal planar rarefaction waves with two axes of symmetry for the Euler equations in two space dimensions, in the case where the initial rarefaction waves are large. The bi-symmetric initial data is a basic type of four-wave two-dimensional Riemann problems. The solutions in this case are continuous, bounded and self-similar, and we characterize how large the rarefaction waves must be. We use the methods of hodograph transformation, characteristic decomposition, and phase space analysis. We resolve binary interactions of simple waves in the process.