Homogenization of Stokes System using Bloch Waves
Analysis of PDEs
2016-08-29 v1
Abstract
In this work, we study the Bloch wave homogenization for the Stokes system with periodic viscosity coefficient. In particular, we obtain the spectral interpretation of the homogenized tensor. The presence of the incompressibility constraint in the model raises new issues linking the homogenized tensor and the Bloch spectral data. The main difficulty is a lack of smoothness for the bottom of the Bloch spectrum, a phenomenon which is not present in the case of the elasticity system. This issue is solved in the present work, completing the homogenization process of the Stokes system via the Bloch wave method.
Keywords
Cite
@article{arxiv.1608.07523,
title = {Homogenization of Stokes System using Bloch Waves},
author = {Grégoire Allaire and Tuhin Ghosh and Muthusamy Vanninathan},
journal= {arXiv preprint arXiv:1608.07523},
year = {2016}
}