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
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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
—
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