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Inverse of divergence and homogenization of compressible Navier-Stokes equations in randomly perforated domains
- Publication Year :
- 2021
-
Abstract
- We analyze behavior of weak solutions to compressible fluid flows in a bounded domain in $\mathbb{R}^3$, randomly perforated by tiny balls with random size. Assuming the radii of the balls scale like $\varepsilon^\alpha$, $\alpha > 3$, with $\varepsilon$ denoting the average distance between the balls, the problem homogenize with the same limiting equation. Our main contribution is a construction of the Bogovski\u{\i} operator, uniformly in $\varepsilon$, without any assumptions on the minimal distance between the balls.<br />Comment: Corrected moment bound assumption on the radii
- Subjects :
- Mathematics - Analysis of PDEs
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2103.04323
- Document Type :
- Working Paper