  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.
