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Non-uniqueness of delta shocks and contact discontinuities in the multi-dimensional model of Chaplygin gas
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SYSNO ASEP 0539553 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Non-uniqueness of delta shocks and contact discontinuities in the multi-dimensional model of Chaplygin gas Author(s) Březina, J. (JP)
Kreml, Ondřej (MU-W) RID, SAI, ORCID
Mácha, Václav (MU-W) RID, SAI, ORCIDArticle number 13 Source Title Nodea-Nonlinear Differential Equations and Applications. - : Springer - ISSN 1021-9722
Roč. 28, č. 2 (2021)Number of pages 24 s. Language eng - English Country CH - Switzerland Keywords admissible weak solution ; Chaplygin gas ; Delta shock ; maximal dissipation Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GJ17-01694Y GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000614045900001 EID SCOPUS 85100334553 DOI 10.1007/s00030-021-00672-0 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2022 Electronic address https://doi.org/10.1007/s00030-021-00672-0
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