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

Diening L, Feireisl E, Lu Y (2017)
ESAIM. Control, Optimisation and Calculus of Variations 23(3): 851-868.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Diening, LarsUniBi ; Feireisl, Eduard; Lu, Yong
Einrichtung
Abstract / Bemerkung
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 $L^p(\Omega)$ 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.
Erscheinungsjahr
2017
Zeitschriftentitel
ESAIM. Control, Optimisation and Calculus of Variations
Band
23
Ausgabe
3
Seite(n)
851-868
ISSN
1292-8119
Page URI
https://pub.uni-bielefeld.de/record/2913486

### Zitieren

Diening L, Feireisl E, 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. 2017;23(3):851-868.
Diening, L., Feireisl, E., & Lu, Y. (2017). 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, 23(3), 851-868. doi:10.1051/cocv/2016016
Diening, L., Feireisl, E., and Lu, Y. (2017). 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 23, 851-868.
Diening, L., Feireisl, E., & Lu, Y., 2017. 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, 23(3), p 851-868.
L. Diening, E. Feireisl, and Y. Lu, “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, vol. 23, 2017, pp. 851-868.
Diening, L., Feireisl, E., 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. 23, 851-868 (2017).
Diening, Lars, Feireisl, Eduard, and 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 23.3 (2017): 851-868.

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arXiv: 1509.09269