slideshow 3

Seminar on partial differential equations

Non-uniqueness of entropy solutions to the 2-d Riemann problem for the Euler equations

Simon Markfelder
Julius-Maximilians-Universität Würzburg

 

Tuesday, 20. March 2018 - 9:00 to 10:00

in IM, rear building, ground floor

In this talk we consider the compressible (full) Euler equations in two space dimensions together with Riemann initial data. The issue of the talk is the question on uniqueness of weak entropy solutions to this problem. This issue has been studied for the isentropic Euler equations by E. Chiodaroli, C. De Lellis and O. Kreml (among others) and the aim is now to extend the results to full (i.e. non-isentropic) Euler. We consider a special class of Riemann data, namely those for which the 1-d self-similar solution consists of two shocks and possibly a contact discontinuity. We show that for this class there exist infinitely many weak entropy solutions, which are generated by convex integration. This is joint work with H. Al Baba, C. Klingenberg, O. Kreml and V. Mácha.