  We consider the unsteady compressible Navier-Stokes equations in a perforated
three-dimensional domain, and show that the limit system for the diameter of
the holes going to zero is the same as in the perforated domain provided the
perforations are small enough. The novelty of this result is the lower
adiabatic exponent $\gamma>3$ instead of the known value $\gamma>6$. The proof
is based on the use of two different restriction operators leading to two
different types of pressure estimates. We also discuss the extension of this
result for the unsteady Navier-Stokes-Fourier system as well as the optimality
of the known results in arbitrary space dimension for both steady and unsteady
problems.
