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

2015/09/30 by Diening, Lars, Feireisl, Eduard, Lu, Yong · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1509.09269

Abstract

We study the inverse of the divergence operator on a domain Ω⊂ R³ perforated by a system of tiny holes. We show that such inverse can be constructed on the Lebesgue space L^p(Ω) 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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• Navier-Stokes-Cahn-Hilliard system in a 3D perforated domain with free slip and source term: Existence and homogenization
• Modeling non-Newtonian fluids in a thin domain perforated with cylinders of small diameter

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