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. 

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

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

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

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

Homogenization of Stokes Equations in Perforated Domains: A Unified Approach

  • Yong Lu
  • Mathematics
    Journal of Mathematical Fluid Mechanics
  • 2020
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

  • Yong Lu
  • Mathematics
    Journal of Mathematical Fluid Mechanics
  • 2020
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

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

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

. 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

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

References

SHOWING 1-10 OF 27 REFERENCES

Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes I. Abstract framework, a volume distribution of holes

This paper treats the homogenization of the Stokes or Navier-Stokes equations with a Dirichlet boundary condition in a domain containing many tiny solid obstacles, periodically distributed in each

Homogenization of the compressible Navier–Stokes equations in a porous medium

We study the homogenization of the compressible Navier–Stokes system in a periodic porous medium (of period e ) with Dirichlet boundary conditions. At the limit, we recover different systems

Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes II: Non-critical sizes of the holes for a volume distribution and a surface distribution of holes

This paper is devoted to the homogenization of the Stokes or Navier-Stokes equations with a Dirichlet boundary condition in a domain containing many tiny solid obstacles, periodically distributed in

Homogenization of nonstationary Navier-Stokes equations in a domain with a grained boundary

SummaryWe prove the convergence of the homogenization process for a nonstationary Navier-Stokes system in a porous medium. The result of homogenization is Darcy's law, as in the case of the Stokes

Compressible Navier-Stokes equations

Compressible, stationary Navier-Stokes (N-S) equations are considered. The shape sensitivity analysis is performed in the case of small perturbations of the so-called it approximate solutions. The

On the Existence of Globally Defined Weak Solutions to the Navier—Stokes Equations

Abstract. We prove the existence of globally defined weak solutions to the Navier—Stokes equations of compressible isentropic flows in three space dimensions on condition that the adiabatic constant

Homogenization of the evolutionary Navier–Stokes system

We study the homogenization problem for the evolutionary Navier–Stokes system under the critical size of obstacles. Convergence towards the limit system of Brinkman’s type is shown under very mild

Homogenization of the stokes flow in a connected porous medium

In this paper we prove the convergence of the homogenization process of the Stokes equations with Dirichlet boundary condition in a periodic porous medium. We consider here the case where the solid