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Texas A&M University
Mathematics

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.