Homogenization of the unsteady compressible Navier-Stokes equations for adiabatic exponent γ > 3

0576363 - MÚ 2024 RIV NL eng J - Journal Article
Oschmann, Florian - Pokorný, M.
Homogenization of the unsteady compressible Navier-Stokes equations for adiabatic exponent γ > 3.
Journal of Differential Equations. Roč. 377, December (2023), s. 271-296. ISSN 0022-0396. E-ISSN 1090-2732
R&D Projects: GA ČR(CZ) GA22-01591S
Institutional support: RVO:67985840
Keywords : Navier-Stokes-Fourier system * compressible Navier-Stokes equations
OECD category: Pure mathematics
Impact factor: 2.4, year: 2022
Method of publishing: Limited access
https://doi.org/10.1016/j.jde.2023.08.040

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 γ>3 instead of the known value γ>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.
Permanent Link: https://hdl.handle.net/11104/0345932