THREE-DIMENSIONAL INTERACTION OF SHOCKS IN IRROTATIONAL FLOWS

Q4 Mathematics

Confluentes Mathematici Pub Date : 2011-11-20 DOI:10.1142/S1793744211000394

D. Serre

引用次数: 6

Abstract

The general d-dimensional Riemann problem raises naturally the question of resolving the interaction of d planar shocks merging at a point. In gas dynamics, we may consider only standing shocks. This problem has received a satisfactory answer in dimension d = 2 (see [3, 4]). We investigate the 3-dimensional case. We restrict to the irrotational case, in order to keep the complexity of the solution within reasonable bounds. We show that a new kind of waves appears downstream, which we call a conical wave. When the equation of state is that of Chaplygin/von Karman, we give a complete mathematical answer to this problem. This involves the existence and uniqueness of a complete minimal surface in a hyperbolic space, with prescribed asymptotics.

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无旋流中激波的三维相互作用

一般的d维黎曼问题自然提出了解决d平面冲击在一点合并的相互作用的问题。在气体动力学中，我们可以只考虑静震。这个问题在维数d = 2中得到了满意的答案(见[3,4])。我们研究三维的情况。为了使解的复杂度保持在合理的范围内，我们将其限制在无旋转情况下。我们展示了一种新的波在下游出现，我们称之为锥形波。当状态方程为Chaplygin/von Karman状态方程时，给出了该问题的完整数学解。这涉及到双曲空间中具有规定渐近的完全极小曲面的存在性和唯一性。

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

Confluentes Mathematici Mathematics-Mathematics (miscellaneous)

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Confluentes Mathematici is a mathematical research journal. Since its creation in 2009 by the Institut Camille Jordan UMR 5208 and the Unité de Mathématiques Pures et Appliquées UMR 5669 of the Université de Lyon, it reflects the wish of the mathematical community of Lyon—Saint-Étienne to participate in the new forms of scientific edittion. The journal is electronic only, fully open acces and without author charges. The journal aims to publish high quality mathematical research articles in English, French or German. All domains of Mathematics (pure and applied) and Mathematical Physics will be considered, as well as the History of Mathematics. Confluentes Mathematici also publishes survey articles. Authors are asked to pay particular attention to the expository style of their article, in order to be understood by all the communities concerned.