Maximal dissipation and well-posedness for the compressible Euler system

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F14%3A00430551" target="_blank" >RIV/67985840:_____/14:00430551 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00021-014-0163-8" target="_blank" >http://dx.doi.org/10.1007/s00021-014-0163-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00021-014-0163-8" target="_blank" >10.1007/s00021-014-0163-8</a>

Result language
angličtina
Original language name
Maximal dissipation and well-posedness for the compressible Euler system
Original language description
We discuss the problem of well-posedness of the compressible (barotropic) Euler system in the framework of weak solutions. The principle of maximal dissipation introduced by C.M. Dafermos is adapted and combined with the concept of admissible weak solutions. We use the method of convex integration in the spirit of the recent work of C.DeLellis and L.Sz´ekelyhidi to show various counterexamples to well-posedness. On the other hand, we conjecture that the principle of maximal dissipation should be retained as a possible criterion of uniqueness as it is violated by the oscillatory solutions obtained in the process of convex integration.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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