Well/ill posedness for the Euler-Korteweg-Poisson system and related problems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F15%3A00443854" target="_blank" >RIV/67985840:_____/15:00443854 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1080/03605302.2014.972517" target="_blank" >http://dx.doi.org/10.1080/03605302.2014.972517</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/03605302.2014.972517" target="_blank" >10.1080/03605302.2014.972517</a>

Result language
angličtina
Original language name
Well/ill posedness for the Euler-Korteweg-Poisson system and related problems
Original language description
We consider a general Euler-Korteweg-Poisson system in R3, supplemented with the space periodic boundary conditions, where the quantum hydrodynamics equations and the classical fluid dynamics equations with capillarity are recovered as particular examples. We show that the system admits infinitely many global-intime weak solutions for any sufficiently smooth initial data including the case of a vanishing initial density - the vacuum zones. Moreover, there is a vast family of initial data, for which theCauchy problem possesses infinitely many dissipative weak solutions, i.e. the weak solutions satisfying the energy inequality. Finally, we establish the weak-strong uniqueness property in a class of solutions without vacuum. In this paper we show that, even in presence of a dispersive tensor, we have the same phenomena found by De Lellis and Székelyhidi.
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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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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