Emmy Noether Lectures

1998 Lecturer: Cathleen Synge Morawetz

Variations on Conservation Laws for the Wave Equation

Cathleen Synge Morawetz: 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 Ph.D. at New York University, with a thesis on the stability of a spherical implosion. She is Professor Emerita at the Courant Institute of Mathematics 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. In 1983, she presented the AWM annual Noether Lecture at the (U.S.) Joint Mathematics Meetings. 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. She was the second woman president of the AMS, serving from 1995 to 1997.
Morawetz’s earliest published works were on the stability of steady viscous flows. In the fifties, she turned to the mathematics of transonic flow, and showed that specially designed shockless airfoils develop shocks if they are altered even by a small amount. The discovery opened the problem of developing a theory for transonic flow with shocks.
Much of her 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 weightless particles moving along ray. With D. Ludwig, Morawetz showed that this is 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 semilinear wave equation. Throughout her career, Morawetz has turned to developments in computations working with A. Bayliss, G. Kriegsman, and T. Wolfe. In her Noether Lecture, she 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 on the propagation of waves.
Morawetz’s father was 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 Motawetz to pursue a Ph.D. in mathematics. A mother of four, Morawetz has been able to balance her energies between her research and her family. She was honored by the National Organization for Women for successfully combining career and family; today her main nonmathematical interests are her six grandchildren – and even there she likes to do things which keep them interested in science and mathematics.