Her uncle was Edward Hutchinson Synge who is credited as the inventor of the Near-field scanning optical microscope and very large astronomical telescopes, based on multiple mirrors.

Morawetz got a job at New York University where she edited Supersonic Flow and Shock Waves by Richard Courant and Kurt Otto Friedrichs.

She published work on a variety of topics in applied mathematics including viscosity, compressible fluids and transonic flows.

Turning to the mathematics of transonic flow, she showed that specially designed shockless airfoils could not, in fact, prevent shocks.

At this point she began to work more closely with her colleagues publishing important joint papers with Peter Lax and Ralph Phillips on the decay of solutions to the wave equation around a star shaped obstacle.

She continued with important solo work on the wave equation and transonic flow around a profile until she was promoted to full professor by 1965.

[3] In 1996, she was awarded an honorary ScD degree by Trinity College Dublin, where her father JL Synge had been a student and later a faculty member.

[15] Morawetz was a member of the National Academy of Sciences[16] and was the first woman to belong to the Applied Mathematics Section of that organization.

Their children are Pegeen Rubinstein, John, Lida Jeck, and Nancy Morawetz (a professor at New York University School of Law who manages its Immigrant Rights Clinic).

Upon being honored by the National Organization for Women for successfully combining career and family, Morawetz quipped, "Maybe I became a mathematician because I was so crummy at housework."