Morawetz's Contributions to the Mathematical Theory of Transonic Flows, Shock Waves, and Partial Differential Equations of Mixed Type
arXiv:2310.07097 · doi:10.1090/bull/1816
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.
8 pages, 4 figures; Bulletin of the American Mathematical Society, 2024 (to appear)