The 2-d isentropic compressible Euler equations may have infinitely many solutions which conserve energy
Analysis of PDEs
2019-01-21 v1
Abstract
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 initial data for which there exist infinitely many weak solutions that fulfill an energy inequality. In this note we will prove that there is Riemann initial data for which there exist infinitely many weak solutions that conserve energy, i.e. they fulfill an energy equality. As in the aforementioned paper we will also show that there even exists Lipschitz initial data with the same property.
Keywords
Cite
@article{arxiv.1709.04982,
title = {The 2-d isentropic compressible Euler equations may have infinitely many solutions which conserve energy},
author = {Simon Markfelder and Christian Klingenberg},
journal= {arXiv preprint arXiv:1709.04982},
year = {2019}
}