莫拉维兹对跨音速流动、激波和混合型偏微分方程的数学理论的贡献

IF 2 3区数学 Q1 MATHEMATICS

Bulletin of the American Mathematical Society Pub Date : 2023-10-19 DOI:10.1090/bull/1816

Gui-Qiang Chen

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引用次数: 0

摘要

本文综述了kathleen Morawetz在跨音速流动、激波和混合椭圆-双曲型偏微分方程数学理论方面的贡献。主要的焦点是Morawetz关于不存在连续跨声速流过剖面的基本工作，Morawetz关于通过补偿紧性构造全局稳定弱跨声速流过剖面的方案，以及楔形激波的规则反射和马赫反射的潜在理论。本文还讨论了Morawetz的工作对这些研究方向和相关领域在纯数学和应用数学中的最新发展和突破的深刻影响。

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Morawetz’s contributions to the mathematical theory of transonic flows, shock waves, and partial differential equations of mixed type

This article is a survey of Cathleen Morawetz’s contributions to the mathematical theory of transonic flows, shock waves, and partial differential equations of mixed elliptic-hyperbolic type. The main focus is on Morawetz’s fundamental work on the nonexistence of continuous transonic flows past profiles, Morawetz’s program regarding the construction of global steady weak transonic flow solutions past profiles via compensated compactness, and a potential theory for regular and Mach reflection of a shock at a wedge. The profound impact of Morawetz’s work on recent developments and breakthroughs in these research directions and related areas in pure and applied mathematics are also discussed.

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来源期刊

Bulletin of the American Mathematical Society 数学-数学

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.