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arXiv · 1509.09269

The inverse of the divergence operator on perforated domains with applications to homogenization problems for the compressible Navier-Stokes system

Lars Diening·Eduard Feireisl·Yong Lu
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Abstract

We study the inverse of the divergence operator on a domain $\Omega \subset R^3$ perforated by a system of tiny holes. We show that such inverse can be constructed on the Lebesgue space $L^p(\Omega)$ for any $1< p < 3$, with a norm independent of perforation, provided the holes are suitably small and their mutual distance suitably large. Applications are given to problems arising in homogenization of steady compressible fluid flows.

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Lars Diening, Eduard Feireisl, Yong Lu. 2015-09-30. The inverse of the divergence operator on perforated domains with applications to homogenization problems for the compressible Navier-Stokes system. https://arxiv.org/abs/1509.09269

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