On wild solutions to the compressible Euler system
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00643399" target="_blank" >RIV/67985840:_____/25:00643399 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-032-02299-8_1" target="_blank" >http://dx.doi.org/10.1007/978-3-032-02299-8_1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-032-02299-8_1" target="_blank" >10.1007/978-3-032-02299-8_1</a>
Alternative languages
Result language
angličtina
Original language name
On wild solutions to the compressible Euler system
Original language description
In this chapter, we survey recent results concerning the existence and properties of so-called wild solutions to the compressible Euler system in two spatial dimensions. These solutions are constructed using the convex integration method developed in this context by De Lellis and Székelyhidi (Ann Math 170:1417–1436,2009, Arch Rational Mech Anal 195:225-260, 2010). We introduce the Riemann problem for the compressible Euler system, classify its one-dimensional self-similar solutions, and summarize results related to the uniqueness and nonuniqueness of these solutions within the class of admissible weak solutions. We also discuss the existence of wild solutions for regular initial data and the failure of criteria based on maximal dissipation of energy to select physically relevant solutions.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Stochastics in Fluids: The 2023 Prague-Sum Workshop Lectures
ISBN
978-3-032-02298-1
ISSN
2510-1374
e-ISSN
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Number of pages
33
Pages from-to
1-33
Publisher name
Birkhäuser
Place of publication
Cham
Event location
Prague
Event date
Aug 21, 2023
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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