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

TL;DR

This survey highlights Cathleen Morawetz's influential work on transonic flows, shock waves, and mixed-type PDEs, emphasizing her foundational results and their impact on mathematical fluid dynamics.

Contribution

The paper reviews Morawetz's pioneering contributions to the non-existence of certain transonic flows, construction of weak solutions via compensated compactness, and shock reflection theory.

Findings

Proved non-existence of continuous transonic flows past profiles.

Developed a program for constructing global weak solutions.

Analyzed shock reflection phenomena using potential theory.

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.