  The main objects of the present work are the quantum Navier-Stokes and
quantum Euler systems; for the first one, in particular, we will consider
constant viscosity coefficients. We deal with the concept of dissipative
solutions, for which we will first prove the weak-strong uniqueness principle
and afterwards, we will show the global existence for any finite energy initial
data. Finally, we will prove that both systems admit a semiflow selection in
the class of dissipative solutions.
