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Well/ill posedness for the Euler-Korteweg-Poisson system and related problems
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SYSNO ASEP 0443854 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Well/ill posedness for the Euler-Korteweg-Poisson system and related problems Tvůrce(i) Donatelli, D. (IT)
Feireisl, Eduard (MU-W) RID, SAI, ORCID
Marcati, P. (IT)Zdroj.dok. Communications in Partial Differential Equations. - : Taylor & Francis - ISSN 0360-5302
Roč. 40, č. 7 (2015), s. 1314-1335Poč.str. 22 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova convex integration ; Euler-Korteweg system ; quantum hydrodynamics Vědní obor RIV BA - Obecná matematika Institucionální podpora MU-W - RVO:67985840 UT WOS 000353691700005 EID SCOPUS 84944443908 DOI 10.1080/03605302.2014.972517 Anotace 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. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2016
Počet záznamů: 1