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

Chen, Gui-Qiang

doi:10.1090/bull/1816

Morawetz’s contributions to the mathematical theory of transonic flows, shock waves, and partial differential equations of mixed type
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by Gui-Qiang G. Chen

Bull. Amer. Math. Soc. 61 (2024), 161-171

DOI: https://doi.org/10.1090/bull/1816

Published electronically: October 19, 2023

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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 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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Bibliographic Information

Gui-Qiang G. Chen
Affiliation: Oxford Centre for Nonlinear Partial Differential Equations, Mathematical Institute, University of Oxford, Oxford, OX2 6GG, United Kingdom
MR Author ID: 249262
ORCID: 0000-0001-5146-3839
Email: chengq@maths.ox.ac.uk
Published electronically: October 19, 2023
Journal: Bull. Amer. Math. Soc. 61 (2024), 161-171
DOI: https://doi.org/10.1090/bull/1816
MathSciNet review: 4678575