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

Abstract

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.

published version

References in corpus (4)

• Homogenization problems for the compressible Navier-Stokes system in 2D perforated domains
• Homogenization of evolutionary incompressible Navier-Stokes system in perforated domains
• Homogenization of the two-dimensional evolutionary compressible Navier-Stokes equations
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