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            <title xml:lang="en">Modeling of a micropolar thin film flow with rapidly varying thickness and non-standard boundary conditions</title>
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                <forename type="first">María</forename>
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                <forename type="first">Francisco J.</forename>
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                <title xml:lang="en">Modeling of a micropolar thin film flow with rapidly varying thickness and non-standard boundary conditions</title>
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                    <forename type="first">María</forename>
                    <surname>Anguiano</surname>
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                    <forename type="first">Francisco J.</forename>
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                <term xml:lang="en">AMS classification numbers: 35B27</term>
                <term xml:lang="en">35Q35</term>
                <term xml:lang="en">76A05</term>
                <term xml:lang="en">76M50</term>
                <term xml:lang="en">76A20 micropolar fluid thin-film flow rapidly oscillating boundary nonzero boundary conditions homogenization</term>
                <term xml:lang="en">76A20 micropolar fluid</term>
                <term xml:lang="en">thin-film flow</term>
                <term xml:lang="en">rapidly oscillating boundary</term>
                <term xml:lang="en">nonzero boundary conditions</term>
                <term xml:lang="en">homogenization</term>
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              <p>In this paper, we study the asymptotic behavior of the micropolar fluid flow through a thin domain assuming zero Dirichlet boundary condition on the top boundary, which is rapidly oscillating, and non- standard boundary conditions on the flat bottom. Assuming “Reynolds roughness regime”, in which the thickness of the domain is very small compared to the wavelenth of the roughness (i.e. a very slight roughness), we rigorously derive a generalized Reynolds equation for pressure clearly showing the roughness-induced effects. Moreover, we give expressions for the average velocity and microrotation.</p>
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