On convergence of approximate solutions to the compressible Euler system

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00532187" target="_blank" >RIV/67985840:_____/20:00532187 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s40818-020-00086-8" target="_blank" >https://doi.org/10.1007/s40818-020-00086-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s40818-020-00086-8" target="_blank" >10.1007/s40818-020-00086-8</a>

Result language
angličtina
Original language name
On convergence of approximate solutions to the compressible Euler system
Original language description
We consider a sequence of approximate solutions to the compressible Euler system admitting uniform energy bounds and/or satisfying the relevant field equations modulo an error vanishing in the asymptotic limit. We show that such a sequence either (i) converges strongly in the energy norm, or (ii) the limit is not a weak solution of the associated Euler system. This is in sharp contrast to the incompressible case, where (oscillatory) approximate solutions may converge weakly to solutions of the Euler system. Our approach leans on identifying a system of differential equations satisfied by the associated turbulent defect measure and showing that it only has a trivial solution.
Czech name
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Czech description
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Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

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

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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