Related papers: Homogenization of the Stokes system in a non-perio…

We consider the homogenization of a Poisson problem or a Stokes system in a randomly punctured domain with Dirichlet boundary conditions. We assume that the holes are spherical and have random centres and radii. We impose that the average…

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 understood, following the classical…

We study the Poisson equation in a perforated domain with homogeneous Dirichlet boundary conditions. The size of the perforations is denoted by $\epsilon$ > 0, and is proportional to the distance between neighbouring perforations. In the…

We consider the homogenization to the Brinkman equations for the incompressible Stokes equations in a bounded domain which is perforated by a random collection of small spherical holes. This problem has been studied by the same authors in…

We consider the homogenisation of the Stokes equations in a porous medium which is evolving in time. At the interface of the pore space and the solid part, we prescribe an inhomogeneous Dirichlet boundary condition, which enables to model a…

We prove the homogenization to the Brinkman equations for the incompressible Stokes equations in a bounded domain which is perforated by a random collection of small spherical holes. The fluid satisfies a no-slip boundary condition at the…

We consider the homogenization of the Stokes equations in a domain perforated with a large number of small holes which are periodically distributed. In [1,2], Allaire gave a systematic study on this problem. In this paper, we introduce a…

We consider the homogenisation of the instationary Stokes equations in a porous medium with an a-priori given evolving microstructure. In order to pass to the homogenisation limit, we transform the Stokes equations to a domain with a fixed…

This paper provides the first study of the homogenization of the 3D non-homogeneous incompressible Navier--Stokes system in perforated domains with holes of supercritical size. The diameter of the holes is of order $\varepsilon^{\alpha} \…

This paper deals with the homogenization of the Poisson equation in a bounded domain of $\mathbb{R}^d$, $d>2$, which is perforated by a random number of small spherical holes with random radii and positions. We show that for a class of…

We study the homogenization of the Poisson equation in randomly perforated domains and obtain the strange term effect in the homogenized equation. The perforations are modeled by rescaled germ-grain processes, and the main assumption is…

In this paper, we study the homogenization of 3D non-homogeneous incompressible Navier-Stokes system in perforated domains with holes of critical size. The diameter of the holes is of size \epsilon^3, where \epsilon is a small parameter…

We consider the Stokes equations on a bounded perforated domaincompleted with non-zero constant boundary conditions on the holes. We investigate configurations forwhich the holes are identical spheres and their number N goes to infinity…

We study a Stokes system posed in a thin perforated layer with a Navier-slip condition on the internal oscillating boundary from two viewpoints: 1) dimensional reduction of the layer and 2) homogenization of the perforated structure.…

We consider the solutions $\rho_\varepsilon, \mathbf{u}_\varepsilon$ to the compressible Navier-Stokes equations (NSE) in a domain periodically perforated by holes of diameter $\varepsilon>0$. We focus on the case where the diameter of the…

The two dimensional Navier-Stokes equation in a perforated domain with a dynamical slip boundary condition is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic…

We study the convergence of the Method of Reflections for the Dirichlet problem of the Poisson and the Stokes equations in perforated domains which consist in the exterior of balls. We prove that the method converges if the balls are…

We revisit the homogenization problem for the Poisson equation in periodically perforated domains with zero Neumann data at the boundary of the holes and prescribed Dirichlet data at the outer boundary. It is known that, if the periodicity…

In this paper, we consider the homogenization of stationary and evolutionary incompressible viscous non-Newtonian flows of Carreau-Yasuda type in domains perforated with a large number of periodically distributed small holes in…

In this paper, we consider the Stokes equations in a perforated domain. When the number of holes increases while their radius tends to 0, it is proven in [L. Desvillettes, F. Golse and V. Ricci. The mean field limit for solid particles in a…