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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

  • Czech description

Classification

  • 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

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