PreprintCC BY 4.0arXiv
Homogenization of the Stokes equations with slender bodies
Abstract
In this paper we study the convergence of solutions of the Stokes equations in a domain perforated by slender bodies placed on a fixed periodic grid of size 2ε as the size of the bodies goes to zero and the number of bodies goes to infinity. We assume that the width bε of the bodies vanishes faster than the length aε of the particles. We identify the critical scaling regimes for aε and bε and prove that in this case the system is effectively described by the Brinkman equations.
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BibTeX
@misc{hadre2026homogenization,
title = {{Homogenization of the Stokes equations with slender bodies}},
author = {Pascal Hadré and Richard M. Höfer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31480},
eprint = {2610.31480},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31480},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Homogenization of the Stokes equations with slender bodies
AU - Pascal Hadré
AU - Richard M. Höfer
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.31480
UR - https://arxiv.org/abs/2610.31480
AB - In this paper we study the convergence of solutions of the Stokes equations in a domain perforated by slender bodies placed on a fixed periodic grid of size 2ε as the size of the bodies goes to zero and the number of bodies goes to infinity. We assume that the width b_ε of the bodies vanishes faster than the length a_ε of the particles. We identify the critical scaling regimes for a_ε and b_ε and prove that in this case the system is effectively described by the Brinkman equations.
ER -