Shocks make the Riemann problem for the full Euler system in multiple space dimensions ill-posed
Identifikátory výsledku
Kód výsledku v 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>
Výsledek na webu
<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>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Shocks make the Riemann problem for the full Euler system in multiple space dimensions ill-posed
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
Shocks make the Riemann problem for the full Euler system in multiple space dimensions ill-posed
Popis výsledku anglicky
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.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
<a href="/cs/project/GJ17-01694Y" target="_blank" >GJ17-01694Y: Matematická analýza parciálních diferenciálních rovnic popisujících nevazké proudění</a><br>
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2020
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Nonlinearity
ISSN
0951-7715
e-ISSN
—
Svazek periodika
33
Číslo periodika v rámci svazku
12
Stát vydavatele periodika
GB - Spojené království Velké Británie a Severního Irska
Počet stran výsledku
24
Strana od-do
6517-6540
Kód UT WoS článku
000581022400001
EID výsledku v databázi Scopus
2-s2.0-85094596422