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We consider the homogenization problem of the compressible Navier-Stokesequations in a bounded three dimensional domain perforated with very tinyholes. As the number of holes increases to infinity, we show that, if the sizeof the holes is small enough, the homogenized equations are the same as thecompressible Navier-Stokes equations in the homogeneous domain---domain withoutholes. This coincides with the previous studies for the Stokes equations andthe stationary Navier-Stokes equations. It is the first result of this kind inthe instationary barotropic compressible setting. The main technical novelty isthe study of the Bogovskii operator in non-Lipschitz domains.

Homogenization of the compressible Navier-Stokes equations in domains with very tiny holes