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arXiv · 2103.04323

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

Peter Bella·Florian Oschmann
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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.

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Peter Bella, Florian Oschmann. 2021-03-07. Inverse of divergence and homogenization of compressible Navier-Stokes equations in randomly perforated domains. https://arxiv.org/abs/2103.04323

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