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

0534002 - MÚ 2021 RIV GB eng J - Journal Article
Klingenberg, C. - Kreml, Ondřej - Mácha, Václav - Markfelder, S.
Shocks make the Riemann problem for the full Euler system in multiple space dimensions ill-posed.
Nonlinearity. Roč. 33, č. 12 (2020), s. 6517-6540. ISSN 0951-7715. E-ISSN 1361-6544
R&D Projects: GA ČR(CZ) GJ17-01694Y
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : full Euler system * ill-posedness * admissible weak solutions * Riemann problem
OECD category: Pure mathematics
Impact factor: 2.129, year: 2020
Method of publishing: Limited access
https://doi.org/10.1088/1361-6544/aba3b2

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.
Permanent Link: http://hdl.handle.net/11104/0312224