ABSTRACT

Transonic flows arise from various physical phenomena, in particular, the flows around aircrafts at near sonic speed. In this talk, I will focus on Euler equations, which are the most suitable equations to describe shocks in gas dynamics. The equations for steady transonic flows are elliptic-hyperbolic coupled system, as well as of mixed type due to their nonlinearity. The related elliptic equations are often nonstandard, such as involving corner singularities and unboundedness of the domains. I will mainly talk about transonic shocks past wedges. The shock in the transonic flow is treated as a free boundary between the supersonic and the subsonic regions. With delicate elliptic estimates we are able to find transonic solutions and to locate the shock-fronts as small perturbations from constant states.

[Light refreshments will be served outside the venue at 4:00-4:30 pm. Please come and join us.]