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Well/ill posedness for the Euler-Korteweg-Poisson system and related problems
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SYSNO ASEP 0443854 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Well/ill posedness for the Euler-Korteweg-Poisson system and related problems Author(s) Donatelli, D. (IT)
Feireisl, Eduard (MU-W) RID, SAI, ORCID
Marcati, P. (IT)Source Title Communications in Partial Differential Equations. - : Taylor & Francis - ISSN 0360-5302
Roč. 40, č. 7 (2015), s. 1314-1335Number of pages 22 s. Language eng - English Country US - United States Keywords convex integration ; Euler-Korteweg system ; quantum hydrodynamics Subject RIV BA - General Mathematics Institutional support MU-W - RVO:67985840 UT WOS 000353691700005 EID SCOPUS 84944443908 DOI 10.1080/03605302.2014.972517 Annotation 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 the Cauchy 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2016
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