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Mathematical derivation of a Reynolds equation for magneto-micropolar fluid flows through a thin domain

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Abstract

In this paper, we study the asymptotic behavior of the stationary 3D magneto-micropolar fluid flow through a thin domain, whose thickness is given by a parameter \(0<\varepsilon \ll 1\). Assuming that the magnetic Reynolds number is written in terms of the thickness \(\varepsilon \), we prove that there exists a critical magnetic Reynolds number, namely \(Re_m^c=\varepsilon ^{-2}\), such that for every magnetic Reynolds number \(Re_m\) with order smaller or equal than \(Re_m^c\), the magneto-micropolar fluid flow in the thin domain can be modeled asymptotically when \(\varepsilon \) tends to zero by a 2D Reynolds-like model, whose expression is also given.

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Acknowledgements

María and Francisco Javier would like to dedicate this article to María’s father, Julio, for his continued support of our research and our professional careers. Also, the authors would like to thank the anonymous referees for their nice comments that have allowed us to improve this article.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, 41012, Sevilla, Spain

    María Anguiano

  2. Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, 41012, Sevilla, Spain

    Francisco Javier Suárez-Grau

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  1. María Anguiano
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  2. Francisco Javier Suárez-Grau
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Correspondence to Francisco Javier Suárez-Grau.

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To María’s father, Julio, for all his support.

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Anguiano, M., Suárez-Grau, F.J. Mathematical derivation of a Reynolds equation for magneto-micropolar fluid flows through a thin domain. Z. Angew. Math. Phys. 75, 28 (2024). https://doi.org/10.1007/s00033-023-02169-5

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