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

Diening, Lars¹  ; Feireisl, Eduard²  ; Lu, Yong³

¹ Institute of Mathematics, Universität Osnabrück, Albrechtstr. 28a, 49076 Osnabrück, Germany
² Institute of Mathematics of the Academy of Sciences of the Czech Republic, Zitná 25, 115 67 Praha 1, Czech Republic
³ Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha, Czech Republic

ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 3, pp. 851-868.

Résumé

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 $L^p\left(\Omega \right)$ 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.

Détail

Reçu le : 2015-09-29
DOI : 10.1051/cocv/2016016

Classification : 35B27, 35Q30, 35Q35
Keywords: Perforated domains, Bogovskii type operators, homogenization, compressible Navier–Stokes system

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