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Shocks make the Riemann problem for the full Euler system in multiple space dimensions ill-posed

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2020

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Klingenberg, Christian
Kreml, Ondřej
Mácha, Václav

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European Union (EU): 320078

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Nonlinearity. IOP Publishing. 2020, 33(12), S. 6517-6540. ISSN 0951-7715. eISSN 1361-6544. Verfügbar unter: doi: 10.1088/1361-6544/aba3b2

Zusammenfassung

The question of (non-)uniqueness of one-dimensional self-similar solutions to the Riemann problem for hyperbolic systems of gas dynamics in the class of multi-dimensional admissible weak solutions was addressed in recent years in several papers culminating in [17] with the proof that the Riemann problem for the isentropic Euler system with a power law pressure is ill-posed if the one-dimensional self-similar solution contains a shock. Then the natural question arises whether the same holds also for a more involved system of equations, the full Euler system. After the first step in this direction was made in [1], where ill-posedness was proved in the case of two shocks appearing in the self-similar solution, we prove in this paper that the presence of just one shock in the self-similar solution implies the same outcome, i.e. the existence of infinitely many admissible weak solutions to the multi-dimensional problem.

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510 Mathematik

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full Euler system, ill-posedness, admissible weak solutions, shocks, Riemann problem

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ISO 690KLINGENBERG, Christian, Ondřej KREML, Václav MÁCHA, Simon MARKFELDER, 2020. Shocks make the Riemann problem for the full Euler system in multiple space dimensions ill-posed. In: Nonlinearity. IOP Publishing. 2020, 33(12), S. 6517-6540. ISSN 0951-7715. eISSN 1361-6544. Verfügbar unter: doi: 10.1088/1361-6544/aba3b2
BibTex
@article{Klingenberg2020-12-01Shock-71874,
  year={2020},
  doi={10.1088/1361-6544/aba3b2},
  title={Shocks make the Riemann problem for the full Euler system in multiple space dimensions ill-posed},
  number={12},
  volume={33},
  issn={0951-7715},
  journal={Nonlinearity},
  pages={6517--6540},
  author={Klingenberg, Christian and Kreml, Ondřej and Mácha, Václav and Markfelder, Simon}
}
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