Parabolic variant of H-measures in homogenisation of a model problem based on Navier-Stokes equation

H-measures, as originally introduced by Luc Tartar and (independently) Patrick Gerard are well suited for hyperbolic problems. For parabolic problems, some variants should be considered, which would be better adapted to parabolic problems. Recently, we introduced a few parabolic scalings and corresponding variant H-measures, including the existence results, investigating their applicability. Here, we present an application of such a variant in homogenisation, for a model based on nonstationary Stokes (sometimes called linearised Navier-Stokes) system. Besides expressing the homogenised coefficients directly in the terms of variant H-measures corresponding to the oscillating coefficients, we also prove that the homogenised coefficients are symmetric, as originally conjectured by Tartar. (C) 2009 Elsevier Ltd. All rights reserved.