We study the inverse of the divergence operator on a domain perforated by a system of tiny holes. We show that such inverse can be constructed on the Lebesgue space for any , 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.
DOI: 10.1051/cocv/2016016
Mots-clés : Perforated domains, Bogovskii type operators, homogenization, compressible Navier–Stokes system
@article{COCV_2017__23_3_851_0,
author = {Diening, Lars and Feireisl, Eduard and Lu, Yong},
title = {The inverse of the divergence operator on perforated domains with applications to homogenization problems for the compressible {Navier{\textendash}Stokes} system},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {851--868},
publisher = {EDP-Sciences},
volume = {23},
number = {3},
year = {2017},
doi = {10.1051/cocv/2016016},
mrnumber = {3660451},
zbl = {1375.35026},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2016016/}
}
TY - JOUR AU - Diening, Lars AU - Feireisl, Eduard AU - Lu, Yong TI - The inverse of the divergence operator on perforated domains with applications to homogenization problems for the compressible Navier–Stokes system JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 851 EP - 868 VL - 23 IS - 3 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2016016/ DO - 10.1051/cocv/2016016 LA - en ID - COCV_2017__23_3_851_0 ER -
%0 Journal Article %A Diening, Lars %A Feireisl, Eduard %A Lu, Yong %T The inverse of the divergence operator on perforated domains with applications to homogenization problems for the compressible Navier–Stokes system %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 851-868 %V 23 %N 3 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2016016/ %R 10.1051/cocv/2016016 %G en %F COCV_2017__23_3_851_0
Diening, Lars; Feireisl, Eduard; Lu, Yong. The inverse of the divergence operator on perforated domains with applications to homogenization problems for the compressible Navier–Stokes system. ESAIM: Control, Optimisation and Calculus of Variations, Volume 23 (2017) no. 3, pp. 851-868. doi : 10.1051/cocv/2016016. https://www.numdam.org/articles/10.1051/cocv/2016016/
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