# 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.

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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.

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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/2016016Diening, 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