Publikation: Shocks make the Riemann problem for the full Euler system in multiple space dimensions ill-posed
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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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KLINGENBERG, 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/aba3b2BibTex
@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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