HOMOGENIZATION OF STOKES SYSTEM USING BLOCH WAVES

Grégoire Allaire (1) , Tuhin Ghosh (2) , Muthusamy Vanninathan (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 TIFR-CAM - Center for Applicable Mathematics [Bangalore]

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.

Domaines: Equations aux dérivées partielles [math.AP]

Grégoire Allaire, Tuhin Ghosh, Muthusamy Vanninathan. HOMOGENIZATION OF STOKES SYSTEM USING BLOCH WAVES. Networks and Heterogeneous Media, 2017, 12 (4), pp.525-550. ⟨hal-01522262⟩