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

@article{Diening2015TheIO, title={The inverse of the divergence operator on perforated domains with applications to homogenization problems for the compressible Navier–Stokes system}, author={Lars Diening and Eduard Feireisl and Yong Lu}, journal={ESAIM: Control, Optimisation and Calculus of Variations}, year={2015}, volume={23}, pages={851-868} }

We study the inverse of the divergence operator on a domain Ω ⊂ R 3 perforated by a system of tiny holes. We show that such inverse can be constructed on the Lebesgue space L p ( Ω ) 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.

## 22 Citations

### Inverse of divergence and homogenization of compressible Navier-Stokes equations in randomly perforated domains

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We analyze behavior of weak solutions to compressible fluid flows in a bounded domain in R, randomly perforated by tiny balls with random size. Assuming the radii of the balls scale like εα, α > 3,…

### Homogenization of Evolutionary Incompressible Navier–Stokes System in Perforated Domains

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In this paper, we consider the homogenization problems for evolutionary incompressible Navier–Stokes system in three dimensional domains perforated with a large number of small holes which are…

### Homogenization of stationary Navier–Stokes–Fourier system in domains with tiny holes

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### Homogenization of the compressible Navier–Stokes equations in domains with very tiny holes

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### Homogenization of Stokes Equations in Perforated Domains: A Unified Approach

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We consider the homogenization of the Stokes equations in a domain perforated with a large number of small holes which are periodically distributed. Allaire (Arch Ration Mech Anal 113(3):209–259,…

### Homogenization of Stokes Equations in Perforated Domains: A Unified Approach

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We consider the homogenization of the Stokes equations in a domain perforated with a large number of small holes which are periodically distributed. Allaire (Arch Ration Mech Anal 113(3):209–259,…

### Homogenization of Poisson and Stokes equations in the whole space

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We consider the homogenization of the Poisson and the Stokes equations in the whole space perforated with periodically distributed small holes. The periodic homogenization in bounded domains is well…

### Construction of a right inverse for the divergence in non-cylindrical time dependent domains

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We construct a stable right inverse for the divergence operator in non-cylindrical domains in space-time. The domains are assumed to be Hölder regular in space and evolve continuously in time. The…

### Homogenization of the two-dimensional evolutionary compressible Navier-Stokes equations

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. We consider the evolutionary compressible Navier-Stokes equations in a two-di-mensional perforated domain, and show that in the subcritical case of very tiny holes, the density and velocity…

### Darcy’s law as low Mach and homogenization limit of a compressible fluid in perforated domains

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We consider the homogenization limit of the compressible barotropic Navier-Stokes equations in a three-dimensional domain perforated by periodically distributed identical particles. We study the…

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