## How Do Perturbations of the Wave Equation Work

### Denver, Colorado 1983

**CATHLEEN SYNGE MORAWETZ** was born in Toronto of Irish parents. She graduated from the University of Toronto in 1945 and went on to receive her master's degree at the Massachusetts Institute of Technology. She earned her PhD at New York University, with a thesis on the stability of a spherical implosion. She is a professor at the Courant Institute of Mathematical Sciences at NYU, where she served as director from 1984 to 1988. In 1981, she delivered the Gibbs Lecture of The American Mathematical Society, and in 1982 presented an Invited Address at a meeting of the Society for Industrial and Applied Mathematics. She is a member of the National Academy of Sciences and was named Outstanding Woman Scientist for 1993 by the Association for Women in Science. In 1995, she became the second woman elected to the office of president of the American Mathematical Society.

Morawetz's earliest published works were on the stability of steady viscous flows. In an early paper, she showed that there are stable modes for many Orr-Somerfeld two-point boundary value problems coming from the perturbation of steady flows, but these modes slip off to infinity in the limit of zero viscosity. As a result, they are of little interest in analyzing viscosity. Turning to the mathematics of transonic flow, she showed that specially designed shockless airfoils develop shocks if they are altered even by a small amount. This discovery opened the problem of developing a theory for a flow with shocks.

Much of Morawetz's research has focused on the wave equation. The classical problem of whether light should be treated as waves or as streams of particles can be answered, "either will do," if it can be shown that high frequency waves are, asymptotically, streams of particles moving along rays. With D. Ludwig, Morawetz showed that this is generally true for a medium with constant light speed outside a reflecting star-shaped object. She used related methods with Walter Strauss to study the behavior of a nonlinear wave equation. Throughout her career, she has followed developments in computations working with A. Bayliss, G. Kriegsman, and T. Wolfe. In her Noether Lecture, Morawetz showed a film generated by computer of some unexpected nonlinear laser effects. Today, her interests are divided between working in fluid dynamics, mainly the mathematics of transonic flow, and computational work on the propagation of waves.

Morawetz's father, who turned ninety-six years old in 1993, is the mathematician J. L. Synge, and her mother also studied mathematics for a time. Both her parents were supportive of her interest in mathematics and science, and it was a woman mathematician, Cecilia Krieger, who had been a family friend for many years who later encouraged Morawetz to pursue a PhD in mathematics. Morawetz says her father was influential in stimulating her interest in mathematics, but he wondered whether her studying mathematics would be wise "He thought we might fight like the Bernoulli brothers," she says. A mother of four, Morawetz has been able to balance her energies between her research and her family. Upon being honored by the National Organization for Women for successfully combining career and family, she quipped, "Maybe I became a mathematician because I was so crummy at housework." She says her current nonmathematical interests are "grandchildren and sailing."