On oscillatory solutions to the complete Euler system
Analysis of PDEs
2020-06-03 v3
Abstract
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 show that the Cauchy problem is basically ill-posed for the -initial data in the class of weak entropy solutions. As a consequence, there are infinitely many measure-valued solutions for a vast set of initial data. Finally, using the concept of relative energy, we discuss a singular limit problem for the measure-valued solutions, where the Mach and Froude number are proportional to a small parameter.
Cite
@article{arxiv.1710.10918,
title = {On oscillatory solutions to the complete Euler system},
author = {Eduard Feireisl and Christian Klingenberg and Ondřej Kreml and Simon Markfelder},
journal= {arXiv preprint arXiv:1710.10918},
year = {2020}
}