Weekly Seminar (ONLINE via ZOOM)
Finding solutions of the multi-dimensional compressible Euler equations
Christian Klingenberg (University of Würzburg (Germany))
Thu, 15 Oct 2020 • 10:15-11:30h • ONLINE (access data will be published)


This talk will survey some results for the two- or three-space dimensional compressible Euler equations, results both in theory and numerics. We shall present

  • non-uniqueness results of weak entropy solutions for special initial data using convex integration
  • introducing solution concepts beyond weak solutions that allows to show convergence to the incompressible limit of the compressible Euler equations with gravity
  • the relationship between stationary preservation, maintaining vorticity, and asymptotic preserving numerical methods
  • introduce a high order numerical method that holds promise to achieve this.

This is joint work among others with Simon Markfelder, Wasilij Barsukow, Eduard Feireisl and Phil Roe.


[1] W. Barsukow, J. Hohm, C. Klingenberg, and P. L. Roe. The active flux scheme on Cartesian grids and its low Mach number limit. Journal of Scientific Computing 81, pp. 594–622 (2019)

[2] E. Feireisl, C. Klingenberg, O. Kreml, and S. Markfelder. On oscillatory solutions to the complete Euler equations. Journal of Differential Equations 296 (2), pp. 1521-1543 (2020)