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arXiv · 2310.07097

Morawetz's Contributions to the Mathematical Theory of Transonic Flows, Shock Waves, and Partial Differential Equations of Mixed Type

Gui-Qiang G. Chen
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Abstract

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 non-existence 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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Gui-Qiang G. Chen. 2023-10-11. Morawetz's Contributions to the Mathematical Theory of Transonic Flows, Shock Waves, and Partial Differential Equations of Mixed Type. https://doi.org/10.1090/bull%2F1816

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