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

✍ Scribed by Nenad Antonić; Martin Lazar

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
501 KB
Volume
11
Category
Article
ISSN
1468-1218

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✦ Synopsis

H-measures, as originally introduced by Luc Tartar and (independently) Patrick Gérard 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 Hmeasures, 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 Hmeasures corresponding to the oscillating coefficients, we also prove that the homogenised coefficients are symmetric, as originally conjectured by Tartar.

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