Cathleen Morawetz passed away on August 8, 2017, at the age of 94. A native of Toronto, Canada, she spent most of her career at New York University’s Courant Institute. Her honors were many, including the U.S. National Medal of Science, the Steele Prize, and the Birkhoff Prize. She was also a member of the U.S. National Academy of Sciences, president of the American Mathematical Society, fellow of the Royal Society of Canada, an International Congress of Mathematicians Emmy Noether lecturer, and a Josiah Willard Gibbs lecturer.
Cathleen Morawetz, 1923-2017. Image courtesy of New York University.
Cathleen’s early work on the theory of transonic fluid flow—referring to partial differential equations that possess both elliptic and hyperbolic regions—remains the most fundamental mathematical work on this subject. The flow is supersonic in the elliptic region, while a shock wave is created at the boundary between the elliptic and hyperbolic regions. In the 1950s, she used functional-analytic methods to study boundary value problems for such transonic problems. One of Cathleen’s theorems predicts that if a smooth steady irrotational flow exists around an aerodynamic profile, then a smooth steady transonic flow cannot exist around any slightly perturbed profile. Thus, while shock-free transonic flows occur, she proved that they cannot be stable. Cathleen’s predictions were subsequently confirmed through both numerical simulations and actual experiments — shock waves physically appear in the flow past the perturbed profile. This aspect of her work has had an important impact on airfoil design, which attempts to minimize the shocks. She also did fundamental work on magnetohydrodynamic shock structure and other related problems.
Beginning in the 1960s, Cathleen investigated the scattering of linear acoustic and electromagnetic waves off obstacles. This involved studying the asymptotics of the wave equation in an exterior domain with Dirichlet boundary conditions. She developed a series of remarkable energy identities, now collectively known as Morawetz identities, which imply a priori that solutions must decay at certain rates. Some of these identities are related to the conformal invariance of the wave equation. In particular, Cathleen proved that the waves decay exponentially if the obstacle is star-shaped. Her estimates were key ingredients in the development of mathematical scattering theory by Peter Lax and Ralph Phillips. In the 1970s, Cathleen’s estimates inspired the development of microlocal methods at boundaries to guarantee the local exponential decay of energy. In 1968, she also proved a novel radial estimate, which provides decay for positive-mass equations.
That Cathleen’s energy estimates, originally developed for linear problems, have played critical roles in the analysis of nonlinear waves is remarkable. Many mathematicians have used the conformally invariant estimates in the theory of small-amplitude hyperbolic waves, ultimately culminating in the analysis of Einstein’s equations of general relativity. The estimates, and especially the radial estimate, have also been instrumental in the study of large-amplitude waves, including the remarkably subtle work Cathleen conducted with me on the nonlinear Klein-Gordon equation. The use of close analogues of her estimates continues to the present day, for nonlinear Schrödinger and other nonlinear dispersive waves, for instance.
Cathleen was an open and charming person. She was admirably able to bring up four lovely children as her mathematical career was simultaneously taking off. She was one of the key personalities to set the tone of openness, generosity, and scientific excellence at the Courant Institute. Cathleen has been a terrific role model for the mathematical community. She will be sorely missed.