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On oscillatory solutions to the complete Euler system

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Datum

2020

Autor:innen

Feireisl, Eduard
Klingenberg, Christian
Kreml, Ondřej

Herausgeber:innen

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https://doi.org/10.1016/j.jde.2020.01.018
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Angaben zur Forschungsförderung

European Union (EU): 320078

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Open Access-Veröffentlichung

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Mathematik und Statistik: Publikationen
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Published

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Journal of Differential Equations. Elsevier. 2020, 269(2), S. 1521-1543. ISSN 0022-0396. eISSN 1090-2732. Verfügbar unter: doi: 10.1016/j.jde.2020.01.018

Zusammenfassung

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 L∞-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.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Compressible Euler equations, Measure-valued solutions

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ISO 690FEIREISL, Eduard, Christian KLINGENBERG, Ondřej KREML, Simon MARKFELDER, 2020. On oscillatory solutions to the complete Euler system. In: Journal of Differential Equations. Elsevier. 2020, 269(2), S. 1521-1543. ISSN 0022-0396. eISSN 1090-2732. Verfügbar unter: doi: 10.1016/j.jde.2020.01.018
BibTex
@article{Feireisl2020-07oscil-71651,
  year={2020},
  doi={10.1016/j.jde.2020.01.018},
  title={On oscillatory solutions to the complete Euler system},
  number={2},
  volume={269},
  issn={0022-0396},
  journal={Journal of Differential Equations},
  pages={1521--1543},
  author={Feireisl, Eduard and Klingenberg, Christian and Kreml, Ondřej and Markfelder, Simon}
}
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