Non-uniqueness of delta shocks and contact discontinuities in the multi-dimensional model of Chaplygin gas
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Non-uniqueness of delta shocks and contact discontinuities in the multi-dimensional model of Chaplygin gas
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
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
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Nodea-Nonlinear Differential Equations and Applications
ISSN
1021-9722
e-ISSN
1420-9004
Volume of the periodical
28
Issue of the periodical within the volume
2
Country of publishing house
CH - SWITZERLAND
Number of pages
24
Pages from-to
13
UT code for WoS article
000614045900001
EID of the result in the Scopus database
2-s2.0-85100334553