In Memoriam: Professor Emerita Cathleen Synge Morawetz

This is a photograph of Cathleen Synge MorawetzCathleen Synge Morawetz died on August 8, 2017. She was 94 years old.

Cathleen was a leading mathematician who made fundamental and lasting contributions in the field of partial differential equations. She worked on a wide range of problems, making seminal contributions to transonic flow and scattering theory among other topics. In 1956 she solved what was then an engineering mystery, by showing that there is no airfoil design that robustly eliminates shocks at supersonic speeds. In the 60s and 70s she studied the scattering of waves by obstacles and nonlinear scattering theory. The techniques she introduced -- now known as "Morawetz inequalities" and "Morawetz estimates" -- are flexible and widely applicable; as a result, her work has strongly influenced many areas where wave propagation is important, including fluid dynamics and general relativity.

Cathleen was born in Toronto in 1923 to John L. Synge, a distinguished Irish physicist and mathematician, and Eleanor Allen. She graduated from the University of Toronto in 1945, received a master's degree in 1946 at the Massachusetts Institute of Technology, and a Ph.D in 1951 at New York University, under the supervision of Kurt O. Friedrichs. After spending a year at MIT, Cathleen joined NYU's Institute for Mathematics and Mechanics (the precursor of today's Courant Institute of Mathematical Sciences) in 1952 as a Research Associate, and after five years became an Assistant Professor. She remained at NYU throughout her career, and was Director of the Courant Institute from 1984 to 1988 -- the first and only woman Director. She was proud to serve as a role model for generations of young mathematicians.

In addition to her academic positions, Cathleen served as President of the American Mathematical Society 1995-7; was a trustee for the American Mathematical Society, the Alfred P. Sloan Foundation, and Princeton University; and served on numerous advisory committees or boards of organizations including the JSTOR Consortium, the NYC Mayor's Commission on Science and Technology, the NCR Corporation, the National Research Council, and the Dublin Institute for Advanced Studies' School of Theoretical Physics.

Cathleen began her research on transonic flow while she was a Research Associate at NYU. In a series of three celebrated papers in the 1950s, she established that shock free flows about profiles are exceptional in the sense that perturbations of the profile shape or upstream velocity of a shockless flow will result in shock formation. This work also provided important tools for the study of mixed type PDE including ingenious energy estimates and maximum principles for auxiliary functions related to invariances in the equations. Cathleen also explored techniques for producing transonic flows with mild shocks, including artificial viscosity approaches combined with compensated compactness in the 1980s; this entailed finding appropriate entropy pairs and obtaining uniform estimates for small viscosity. In addition, Cathleen opened the door to constructing rich families of shockless 2-D flows by obtaining well posedness for weak solutions of the Dirichlet problem for Tricomi type equations, with a first breakthrough in 1970 and robust refinements some 30 years later.

During the 60s and 70s Cathleen became interested in scattering problems. One focus was the scattering of waves by obstacles, where she proved local energy decay for star-shaped obstacles. The proof was based upon ingenious energy identities, totally different from the usual energy identities of mathematical physics. These identities have been central to modern theories of hyperbolic and mixed-type partial differential equations. This work and subsequent research on nonlinear scattering theory led to a whole series of "Morawetz inequalities" and "Morawetz estimates", both of which refer to a general procedure for proving local energy decay of solutions to a large class of dispersive equations. The applicability of this procedure to a wide range of problems has made Cathleen's work very influential in the study of nonlinear waves, including general relativity.

Cathleen received many honors and awards, including honorary degrees from New York University (2007), the University of Toronto (1996), the University of Dublin (1996), the University of Waterloo (1993), Duke University (1988), New Jersey Institute of Technology (1988), Princeton University (1986), Brown University (1982), Smith College (1980), and Eastern Michigan University (1980). She was elected Fellow of the American mathematical Society (2012), SIAM Fellow (2009), Fellow of the American Philosophical Society (1997); Fellow of the Royal Society of Canada (1996); Member of the National Academy of Sciences (1990); Fellow of the American Academy of Arts and Sciences (1984); and she held Guggenheim Fellowships twice, in 1966-7 and 1978-9.

In 1998 Cathleen received the National Medal of Science. Her other awards include the American Mathematical Society's Leroy P. Steele Prize for Lifetime Achievement (2004), and its George David Birkhoff Prize in Applied Mathematics (2006).

She is survived by her husband Herbert; her children John, Lida, Nancy, and Pegeen; 10 grandchildren and step-granchildren; and 3 great-grandchildren.

Additional information about Cathleen, including video, is available at the Simons Foundation "Science Lives" website.

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