Solution Semiflow to the isentropic Euler system
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00522128" target="_blank" >RIV/67985840:_____/20:00522128 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00205-019-01420-6" target="_blank" >https://doi.org/10.1007/s00205-019-01420-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00205-019-01420-6" target="_blank" >10.1007/s00205-019-01420-6</a>
Alternative languages
Result language
angličtina
Original language name
Solution Semiflow to the isentropic Euler system
Original language description
It is nowadays well understood that the multidimensional isentropic Euler system is desperately ill-posed. Even certain smooth initial data give rise to infinitely many solutions and all available selection criteria fail to ensure both global existence and uniqueness. We propose a different approach to the well-posedness of this system based on ideas from the theory of Markov semigroups: we show the existence of a Borel measurable solution semiflow. To this end, we introduce a notion of dissipative solution which is understood as time dependent trajectories of the basic state variables—the mass density, the linear momentum, and the energy—in a suitable phase space. The underlying system of PDEs is satisfied in a generalized sense. The solution semiflow enjoys the standard semigroup property and the solutions coincide with the strong solutions as long as the latter exist. Moreover, they minimize the energy (maximize the energy dissipation) among all dissipative solutions.
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
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA18-05974S" target="_blank" >GA18-05974S: Oscillations and concentrations versus stability in the equations of mathematical fluid dynamics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Archive for Rational Mechanics and Analysis
ISSN
0003-9527
e-ISSN
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Volume of the periodical
235
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
28
Pages from-to
167-194
UT code for WoS article
000522430900006
EID of the result in the Scopus database
2-s2.0-85069473027