Affordable Access

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

Authors
  • Donatelli, Donatella
  • Feireisl, Eduard
  • Marcati, Pierangelo
Type
Preprint
Publication Date
Aug 21, 2014
Submission Date
Aug 21, 2014
Identifiers
arXiv ID: 1408.5063
Source
arXiv
License
Yellow
External links

Abstract

We consider a general Euler-Korteweg-Poisson system in $R^3$, 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-in-time 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.

Report this publication

Statistics

Seen <100 times