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

Homogenization of the unsteady compressible Navier-Stokes equations for adiabatic exponent $\gamma>3$