Lp estimates for the homogenization of stokes problem in a perforated domain
Analysis of PDEs
2016-11-21 v1
Abstract
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 Navier-Stokes flow. J. Stat. Phys. 131: 941-967, 2008], under suitable dilution assumptions, that the solution is well-approximated asymptotically by solving a Stokes-Brinkman equation. We provide here quantitative estimates in L p-norms of this convergence.
Cite
@article{arxiv.1611.06077,
title = {Lp estimates for the homogenization of stokes problem in a perforated domain},
author = {Amina Mecherbet and Matthieu Hillairet},
journal= {arXiv preprint arXiv:1611.06077},
year = {2016}
}