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Shocks Make the Riemann Problem for the Full Euler System in Multiple Space Dimensions Ill-posed
Christian Klingenberg, Ondřej Kreml, Václav Mácha +1
The question of (non-)uniqueness of one-dimensional self-similar solutions to the Riemann problem for hyperbolic systems of gas dynamics in sets of multi-dimensional admissible wea…
Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations
Simon Markfelder
We shall deal with both the barotropic and the full compressible Euler system in multiple space dimensions. Both systems are particular examples of hyperbolic conservation laws. Wh…
Non-uniqueness of entropy-conserving solutions to the ideal compressible MHD equations
Christian Klingenberg, Simon Markfelder
In this note we consider the ideal compressible magneto-hydrodynamics (MHD) equations in a special two dimensional setting. We show that there exist particular initial data for whi…
On the density of wild initial data for the compressible Euler system
Eduard Feireisl, Christian Klingenberg, Simon Markfelder
We consider a class of wild initial data to the compressible Euler system that give rise to infinitely many admissible weak solutions via the method of convex integration. We ident…
Non-uniqueness of admissible weak solution to the Riemann problem for the full Euler system in 2D
Hind Al Baba, Christian Klingenberg, Ondrej Kreml +2
The question of well- and ill-posedness of entropy admissible solutions to the multi-dimensional systems of conservation laws has been studied recently in the case of isentropic Eu…
On the low Mach number limit for the compressible Euler system
Eduard Feireisl, Christian Klingenberg, Simon Markfelder
In this paper, we propose a new approach to singular limits of inviscid fluid flows based on the concept of dissipative measure-valued solutions. We show that dissipative measure-v…