Analysis of the roughness regimes for micropolar fluids via homogenization

2019/07/01 by Suárez-Grau, Francisco J. · 5 citations
#35B27 #35Q35 #76A05 #76A20 #76D08 #76M50 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.00628

Abstract

We study the asymptotic behavior of micropolar fluid flows in a thin domain of thickness η_ε with a periodic oscillating boundary with wavelength ε. We consider the limit when ε tends to zero and, depending on the limit of the ratio of η_ε/ε, we prove the existence of three different regimes. In each regime, we derive a generalized Reynolds equation taking into account the microstructure of the roughness.

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