Numerical Analysis Seminar
Date: January 31, 2018
Time: 3:00PM - 4:00PM
Location: BLOC 628
Speaker: Christian Klingenberg, Würzburg University
Title: The inititial value problem for the multidimensional system of compressible gas dynamics may have infinitely many weak solutions
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 Lipshitz 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.