Homogenization of the Stokes system in a thin film flow with rapidly varying thickness. (English) Zbl 0675.76033

Summary: We study a problem with two small parameters, that models a fluid flow between two close rough surfaces. We study the convergence by the energy method of the 3-dimensional Stokes system solution when the ratio \(\lambda =\eta /\epsilon\) is constant (\(\eta\) is linked to the fluid thickness and \(\epsilon\) to the size of the roughness period). Then making \(\lambda\) tend to infinity (resp. to zero) we show that the case in which the thickness is greater (resp. smaller) than the period is an asymptotic limit of the intermediate case.


76D07 Stokes and related (Oseen, etc.) flows
76D08 Lubrication theory


Zbl 0675.76036
Full Text: DOI EuDML


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