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.References
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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
- © Copyright 2023 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 61 (2024), 161-171
- DOI: https://doi.org/10.1090/bull/1816
- MathSciNet review: 4678575