Non-uniqueness of delta shocks and contact discontinuities in the multi-dimensional model of Chaplygin gas
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00539553" target="_blank" >RIV/67985840:_____/21:00539553 - isvavai.cz</a>
Výsledek na webu
<a href="https://doi.org/10.1007/s00030-021-00672-0" target="_blank" >https://doi.org/10.1007/s00030-021-00672-0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00030-021-00672-0" target="_blank" >10.1007/s00030-021-00672-0</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Non-uniqueness of delta shocks and contact discontinuities in the multi-dimensional model of Chaplygin gas
Popis výsledku v původním jazyce
We study the Riemann problem for the isentropic compressible Euler equations in two space dimensions with the pressure law describing the Chaplygin gas. It is well known that there are Riemann initial data for which the 1D Riemann problem does not have a classical BV solution, instead a δ-shock appears, which can be viewed as a generalized measure-valued solution with a concentration measure in the density component. We prove that in the case of two space dimensions there exist infinitely many bounded admissible weak solutions starting from the same initial data. Moreover, we show the same property also for a subset of initial data for which the classical 1D Riemann solution consists of two contact discontinuities. As a consequence of the latter result we observe that any criterion based on the principle of maximal dissipation of energy will not pick the classical 1D solution as the physical one. In particular, not only the criterion based on comparing dissipation rates of total energy but also a stronger version based on comparing dissipation measures fails to pick the 1D solution.
Název v anglickém jazyce
Non-uniqueness of delta shocks and contact discontinuities in the multi-dimensional model of Chaplygin gas
Popis výsledku anglicky
We study the Riemann problem for the isentropic compressible Euler equations in two space dimensions with the pressure law describing the Chaplygin gas. It is well known that there are Riemann initial data for which the 1D Riemann problem does not have a classical BV solution, instead a δ-shock appears, which can be viewed as a generalized measure-valued solution with a concentration measure in the density component. We prove that in the case of two space dimensions there exist infinitely many bounded admissible weak solutions starting from the same initial data. Moreover, we show the same property also for a subset of initial data for which the classical 1D Riemann solution consists of two contact discontinuities. As a consequence of the latter result we observe that any criterion based on the principle of maximal dissipation of energy will not pick the classical 1D solution as the physical one. In particular, not only the criterion based on comparing dissipation rates of total energy but also a stronger version based on comparing dissipation measures fails to pick the 1D solution.
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
2021
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Nodea-Nonlinear Differential Equations and Applications
ISSN
1021-9722
e-ISSN
1420-9004
Svazek periodika
28
Číslo periodika v rámci svazku
2
Stát vydavatele periodika
CH - Švýcarská konfederace
Počet stran výsledku
24
Strana od-do
13
Kód UT WoS článku
000614045900001
EID výsledku v databázi Scopus
2-s2.0-85100334553