arXiv subjects

Valentin Pellhammer

Publications and source records attributed to Valentin Pellhammer.

3 recordsLinked to original sources

arXiv2026

The local least action criterion fails as a selection criterion for weak solutions of the compressible Euler equations

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 compressible Euler equations. Indeed, convex integration has shown that admissible weak solutions are in general highly non-unique. This has motivated additional selection criteria intended to rule out the counterintuitive solutions generated by convex integration. In this paper we prove that the local least action criterion introduced by H.~Gimperlein, M.~Grinfeld, R.~J.~Knops and M.~Slemrod does not serve as a proper selection criterion, since it fails to select the solution that is intuitively expected to be physically relevant.

math.AP↗

arXiv2025

Failure of the least action admissibility principle in the context of the compressible Euler equations

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 integration, the classical notion of an admissible weak solutions (also known as weak entropy solutions) does not lead to uniqueness and allows for solutions which do not seem to be physical. For this reason, people have studied additional criteria in view of their ability to rule out the counterintuitive solutions generated by convex integration. Recently, in [H.~Gimperlein, M.~Grinfeld, R.~J.~Knops and M.~Slemrod: The least action admissibility principle, arXiv: 2409.07191 (2024)] it was suggested that the least action admissibility principle serves as the desired selection criterion. In this paper, however, we show that the least action admissibility principle rules out the solution which is intuitively the physically relevant one. Consequently, one either has to reconsider one's intuition, or the least action admissibility principle must be discarded.

math.AP↗

arXiv2023

Oscillating Shock Profiles in Relativistic Fluid Dynamics

This note studies a model for relativistic pure-radiation fluids with viscosity that was recently proposed by Bemfica, Disconzi and Noronha, and shows that there are shock waves whose continuous shock profiles, if existing, are oscillating in any variables. This behavior differs significantly from the situation in classical fluid dynamics, in which canonical state variables are monotone along the shock profile.

math.AP↗