Finding solutions of the multi-dimensional compressible Euler equations
Organized by: FAU DCN-AvH, Chair in Applied Analysis – Alexander von Humboldt Professorship at FAU Erlangen-Nürnberg (Germany)
Speaker: Prof. Dr. Christian Klingenberg
Affiliation: Universität Würzburg (Germany)
Meeting ID: 998 6927 2903 | PIN code: 072804
Abstract. 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
• introduce 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.
 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)
 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)