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Non-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equations

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2018

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Klingenberg, Christian

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https://doi.org/10.1142/s0219891618500224
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Journal of Hyperbolic Differential Equations. World Scientific. 2018, 15(4), S. 721-730. ISSN 0219-8916. eISSN 1793-6993. Verfügbar unter: doi: 10.1142/s0219891618500224

Zusammenfassung

We consider the 2-d isentropic compressible Euler equations. It was shown in [E. Chiodaroli, C. De Lellis and O. Kreml, Global ill-posedness of the isentropic system of gas dynamics, Comm. Pure Appl. Math. 68(7) (2015) 1157–1190] 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 paper, 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 exist Lipschitz initial data with the same property.

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Fachgebiet (DDC)
510 Mathematik

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Non-uniqueness, Compressible Euler equations

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ISO 690KLINGENBERG, Christian, Simon MARKFELDER, 2018. Non-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equations. In: Journal of Hyperbolic Differential Equations. World Scientific. 2018, 15(4), S. 721-730. ISSN 0219-8916. eISSN 1793-6993. Verfügbar unter: doi: 10.1142/s0219891618500224
BibTex
@article{Klingenberg2018-12Nonun-71650,
  year={2018},
  doi={10.1142/s0219891618500224},
  title={Non-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equations},
  number={4},
  volume={15},
  issn={0219-8916},
  journal={Journal of Hyperbolic Differential Equations},
  pages={721--730},
  author={Klingenberg, Christian and Markfelder, Simon}
}
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