Convergence of the pressure in the homogenization of the Stokes equations in randomly perforated domains

We consider the homogenization to the Brinkman equations for the incompressible Stokes equations in a bounded domain which is perforated by a random collection of small spherical holes. This problem has been studied by the same authors in Giunti and Höfer (2019) [7] where convergence of the fluid ve...

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Bibliographic Details
Published in:Journal of Differential Equations 2022-05, Vol.320, p.399-418
Main Authors: Giunti, Arianna, Höfer, Richard M.
Format: Article
Language:English
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Summary:We consider the homogenization to the Brinkman equations for the incompressible Stokes equations in a bounded domain which is perforated by a random collection of small spherical holes. This problem has been studied by the same authors in Giunti and Höfer (2019) [7] where convergence of the fluid velocity field towards the solution of the Brinkman equations has been established. In the present we consider the pressure associated to the solution of the Stokes equations in the perforated domain. We prove that it is possible to extend this pressure inside the holes and slightly modify it in a region of asymptotically negligible harmonic capacity such that it weakly converges to the pressure associated with the solution of the Brinkman equations.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2022.03.003