Cathleen Morawetz

Courant Institute, NYU

Mixed Equations and Some Linear Problems From Transonic Flows

The study of mixed equations goes back to the work of Tricomi in 1923 but became of much greater interest in the 1950s when the possibility of flying close to the speed of sound arose and it was fully recognized that the governing equation was of mixed type, elliptic where the flow was subsonic and hyperbolic where it was supersonic.We shall outline some problems of well-posedness including an application of Noether's conservation law theorem. Most of the talk will be devoted to desired but somewhat anomalous theorems for a linear mixed equation whose solutions would describe perturbations of smooth transonic flows.