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

0475172 - MÚ 2018 FR eng J - Journal Article
Diening, L. - Feireisl, Eduard - Lu, Y.
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. Roč. 23, č. 3 (2017), s. 851-868. ISSN 1292-8119. E-ISSN 1262-3377
Keywords : perforated domains * Bogovskii type operators * homogenization * compressible Navier–Stokes system
OECD category: Applied mathematics
Impact factor: 1.225, year: 2017
https://www.esaim-cocv.org/articles/cocv/abs/2017/03/cocv160016-s/cocv160016-s.html

We study the inverse of the divergence operator on a domain Omega subset of 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.
Permanent Link: http://hdl.handle.net/11104/0272016