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Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial data

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00541167" target="_blank" >RIV/67985840:_____/21:00541167 - isvavai.cz</a>

  • Alternative codes found

    RIV/00216208:11320/21:10441305

  • Result on the web

    <a href="https://doi.org/10.1090/tran/8129" target="_blank" >https://doi.org/10.1090/tran/8129</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1090/tran/8129" target="_blank" >10.1090/tran/8129</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial data

  • Original language description

    We consider the isentropic Euler equations of gas dynamics in the whole two-dimensional space and we prove the existence of a C∞ initial datum which admits infinitely many bounded admissible weak solutions. Taking advantage of the relation between smooth solutions to the Euler system and to the Burgers equation we construct a smooth compression wave which collapses into a perturbed Riemann state at some time instant T > 0. In order to continue the solution after the formation of the discontinuity, we adjust and apply the theory developed by De Lellis and Székelyhidi [Ann. of Math. (2) 170 (2009), no. 3, pp. 1417–1436, Arch. Ration. Mech. Anal. 195 (2010), no. 1, pp. 225–260] and we construct infinitely many solutions. We introduce the notion of an admissible generalized fan subsolution to be able to handle data which are not piecewise constant and we reduce the argument to finding a single generalized subsolution.

  • 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

    American Mathematical Society. Transactions

  • ISSN

    0002-9947

  • e-ISSN

    1088-6850

  • Volume of the periodical

    374

  • Issue of the periodical within the volume

    4

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    27

  • Pages from-to

    2269-2295

  • UT code for WoS article

    000625870700001

  • EID of the result in the Scopus database

    2-s2.0-85094614183