46 citations · 190 across the 19 of their papers we have counts for
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The local least action criterion fails as a selection criterion for weak solutions of the compressible Euler equations
Simon Markfelder, Valentin Pellhammer
It is now well known that the classical notion of admissible weak solutions (also known as weak entropy solutions) does not restore uniqueness for the multi-dimensional compressibl…
Non-uniqueness of global-in-time admissible weak solutions to the isentropic compressible Euler equations for a dense set of initial data
Daniel W. Boutros, Simon Markfelder
In recent years, the technique of convex integration has demonstrated that for some initial data (also referred to as 'wild initial data'), many PDE models of mathematical fluid me…
A Generalized Framework for Convex Integration and its Application to Geophysical Models
Daniel W. Boutros, Simon Markfelder, Edriss S. Titi
In this paper a general framework for convex integration is developed, in order to construct weak solutions to the Cauchy problem, by building on ideas from [C. De Lellis and L. Sz…
Maximal entropy production principle and the Euler system of gas dynamics
Elisabetta Chiodaroli, Eduard Feireisl, Ondřej Kreml +1
Convex integration has revealed that the Euler system of gas dynamics is ill-posed in the class of weak solutions even if the entropy inequality is imposed as an additional constra…
Maximal turbulence as a selection criterion for measure-valued solutions
Christian Klingenberg, Simon Markfelder, Emil Wiedemann
The quest for a good solution concept for the partial differential equations (PDEs) arising in mathematical fluid dynamics is an outstanding open problem. An important notion of so…
Failure of the least action admissibility principle in the context of the compressible Euler equations
Simon Markfelder, Valentin Pellhammer
Finding a proper solution concept for the multi-dimensional barotropic compressible Euler equations and related systems is still an unsolved problem. As revealed by convex integrat…
A New Convex Integration Approach for the Compressible Euler Equations and Failure of the Local Maximal Dissipation Criterion
Simon Markfelder
In this paper we establish a new convex integration approach for the barotropic compressible Euler equations in two space dimensions. In contrast to existing literature, our new me…
Nonuniqueness of generalised weak solutions to the primitive and Prandtl equations
Daniel W. Boutros, Simon Markfelder, Edriss S. Titi
We develop a convex integration scheme for constructing nonunique weak solutions to the hydrostatic Euler equations (also known as the inviscid primitive equations of oceanic and a…
On Energy Conservation for the Hydrostatic Euler Equations: An Onsager Conjecture
Daniel W. Boutros, Simon Markfelder, Edriss S. Titi
Onsager's conjecture, which relates the conservation of energy to the regularity of weak solutions of the Euler equations, was completely resolved in recent years. In this work, we…
Euler system with a polytropic equation of state as a vanishing viscosity limit
Eduard Feireisl, Christian Klingenberg, Simon Markfelder
We consider the Euler system of gas dynamics endowed with the incomplete equation of state relating the internal energy to the mass density and the pressure. We show that any suffi…
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…
On oscillatory solutions to the complete Euler system
Eduard Feireisl, Christian Klingenberg, Ondřej Kreml +1
The Euler system in fluid dynamics is a model of a compressible inviscid fluid incorporating the three basic physical principles: Conservation of mass, momentum, and energy. We sho…
The 2-d isentropic compressible Euler equations may have infinitely many solutions which conserve energy
Simon Markfelder, Christian Klingenberg
We consider the 2-d isentropic compressible Euler equations. It was shown in by E. Chiodaroli, C. De Lellis and O. Kreml that there exist Riemann initial data as well as Lipschitz…
The Riemann problem for the multidimensional isentropic system of gas dynamics is ill-posed if it contains a shock
Christian Klingenberg, Simon Markfelder
In this paper we consider the isentropic compressible Euler equations in two space dimensions together with particular initial data. The latter consists only of two constant states…