**Abstract:**

We consider the isentropic compressible Euler equations in two space dimensions together with particular initial data. This data consists of two constant states only, where one state lies on the lower and the other state on the upper half plane. The aim is to investigate if there exists a unique entropy solution or if the convex integration method produces infinitely many entropy solutions. In this lecture we will show that the solution of this Riemann problem for the 2-d isentropic Euler equations is non-unique (except if the solution is smooth). Next we are able to show that there exist Lipschitz data that may lead to infinitely many solutions even for the full system of Euler equations. This is joint work with Eduard Feireisl and Simon Markfelder.

**Biography:**

Professor Christian Klingenberg is a Professor at Würzburg University, Germany. He obtained his Ph.D. in Courant institute with Professor Cathleen Morawetz. His research interests include compressible gas dynamics, magnetohydrodynamics and kinetic modeling.

*Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai*