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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Communications in Partial Differential Equations

ISSN

0360-5302

e-ISSN

—

Svazek periodika

40

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

1314-1335

Kód UT WoS článku

000353691700005

EID výsledku v databázi Scopus

2-s2.0-84944443908