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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00534002" target="_blank" >RIV/67985840:_____/20:00534002 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1088/1361-6544/aba3b2" target="_blank" >https://doi.org/10.1088/1361-6544/aba3b2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1361-6544/aba3b2" target="_blank" >10.1088/1361-6544/aba3b2</a>

Result language
angličtina
Original language name
Shocks make the Riemann problem for the full Euler system in multiple space dimensions ill-posed
Original language description
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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GJ17-01694Y" target="_blank" >GJ17-01694Y: Mathematical analysis of partial differential equations describing inviscid flows</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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