  In this paper we analyze the large-time behavior of weak solutions to
polytropic fluid models possibly including quantum and capillary effects.
Formal a priori estimates show that the density of solutions to these systems
should disperse with time. Scaling appropriately the system, we prove that,
under a reasonable assumption on the decay of energy, the density of weak
solutions converges in large times to an unknown profile. In contrast with the
isothermal case, we also show that there exists a large variety of asymptotic
profiles. We complement the study by providing existence of global-in-time weak
solutions satisfying the required decay of energy. As a byproduct of our
method, we also obtain results concerning the large-time behavior of solutions
to nonlinear Schr{\"o}dinger equation, allowing the presence of a
semi-classical parameter as well as long range nonlinearities.
