Inverse of divergence and homogenization of compressible Navier-Stokes equations in randomly perforated domains

0569958 - MÚ 2024 RIV DE eng J - Journal Article
Bella, P. - Oschmann, Florian
Inverse of divergence and homogenization of compressible Navier-Stokes equations in randomly perforated domains.
Archive for Rational Mechanics and Analysis. Roč. 247, č. 2 (2023), č. článku 14. ISSN 0003-9527. E-ISSN 1432-0673
Institutional support: RVO:67985840
Keywords : compressible viscous fluid flow * Navier-Stokes equation
OECD category: Pure mathematics
Impact factor: 2.5, year: 2022
Method of publishing: Open access
https://doi.org/10.1007/s00205-023-01847-y

We analyze the behavior of weak solutions to compressible viscous fluid flows in a bounded domain in R3, randomly perforated by tiny balls with random size. Assuming the radii of the balls scale like εα, α> 3 , with ε denoting the average distance between the balls, the problem homogenize to the same limiting equation. Our main contribution is a construction of the Bogovskiĭ operator, uniformly in ε, without any assumptions on the minimal distance between the balls.
Permanent Link: https://hdl.handle.net/11104/0341282