# American Institute of Mathematical Sciences

December  2017, 12(4): 525-550. doi: 10.3934/nhm.2017022

## Homogenization of stokes system using bloch waves

 1 Centre de Mathématiques Appliquées, Ecole Polytechnique, CNRS, Université Paris-Saclay, Palaiseau, France 2 Centre for Applicable Matematics, Tata Institute of Fundamental Research, Bangalore, India 3 Current address: Mathematics Department, IIT-Bombay, Mumbai, India

Received  September 2016 Revised  April 2017 Published  October 2017

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.

Citation: Grégoire Allaire, Tuhin Ghosh, Muthusamy Vanninathan. Homogenization of stokes system using bloch waves. Networks & Heterogeneous Media, 2017, 12 (4) : 525-550. doi: 10.3934/nhm.2017022
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