On the rarefaction waves of the two-dimensional compressible Euler equations for magnetohydrodynamics

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2020-09-01 DOI:10.1142/s0219891620500174

Jianjun Chen, G. Lai, Wancheng Sheng

引用次数: 4

Abstract

The expansion of a wedge of magnetic fluid into vacuum is studied in this paper. The magnetic fluid away from the sharp corner of a wedge expands into the vacuum as two plane-symmetric rarefaction waves, and the problem can be reduced to the interaction of these two rarefaction waves. In order to determine the flow in the interaction zone, we formulate a Goursat problem for the two-dimensional, self-similar Euler equations of magnetohydrodynamic. This system is of mixed type, and the type at each point is determined by the local fluid velocity and the local magneto-acoustic speed. We establish that the system is uniformly hyperbolic in the interaction zone when the half-angle of the wedge is less than some angle [Formula: see text], while the existence of a global classical solution to the Goursat problem is proven by a method of characteristic decomposition.

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磁流体力学二维可压缩Euler方程的稀疏波

本文研究了磁流体楔块在真空中的膨胀。远离楔形尖角的磁流体以两个平面对称的稀疏波的形式膨胀到真空中，这个问题可以归结为这两个稀疏波的相互作用。为了确定相互作用区中的流动，我们为磁流体动力学的二维自相似欧拉方程建立了Goursat问题。该系统是混合型的，每个点的类型由局部流体速度和局部磁声速决定。我们建立了当楔的半角小于某个角度时，系统在相互作用区是一致双曲的[公式：见正文]，同时通过特征分解的方法证明了Goursat问题的全局经典解的存在性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Hyperbolic Differential Equations 数学-物理：数学物理

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in: Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions. Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc. Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations. Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc. General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations. Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.