THE INVERSE OF THE DIVERGENCE OPERATOR ON PERFORATED DOMAINS WITH APPLICATIONS TO HOMOGENIZATION PROBLEMS FOR THE COMPRESSIBLE NAVIER-STOKES SYSTEM

Autor(en): Diening, Lars 
Feireisl, Eduard
Lu, Yong
Stichwörter: Automation & Control Systems; Bogovskii type operators; compressible Navier-Stokes system; EQUATIONS; homogenization; JOHN DOMAINS; Mathematics; Mathematics, Applied; Perforated domains
Erscheinungsdatum: 2017
Herausgeber: EDP SCIENCES S A
Journal: ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
Volumen: 23
Ausgabe: 3
Startseite: 851
Seitenende: 868
Zusammenfassung: 
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.
ISSN: 12928119
DOI: 10.1051/cocv/2016016

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