The seminar is sponsored by NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.

**Abstract:**

We present a characteristic decomposition of the Two-dimensional Euler Equations in the self-similar plane. The decomposition allows for a proof that we construct semi-hyperbolic patches of solutions, in which one family out of two nonlinear families of characteristics starts on sonic curves and ends on transonic shock waves, to the two-dimensional Euler equations. This type of solution appears in the transonic flow over an airfoil and Guderley reflection, and is common in the numerical solutions of Riemann problems.

**Biography:**

Prof. Mingjie Li holds his Ph.D. from Capital Normal University in June 2009. Now he is an assistant professor of College of Science in Minzu University of China. Prof. Li’s research interests are Fluid Mechanics, Nonlinear Partial Differential Equations and Related Applications. His work has appeared in the *Arch. Rational. Mech. Anal., SIAM J. Math. Anal., J. Differential Equations* and so on.