title: Asymptotic behaviour of Stokes flow in a thin domain with a moving rough boundary.
abstract: We consider a problem that models fluid flow in a thin domain bounded by two surfaces. One of the surfaces is rough and moving, whereas the other is flat and stationary. The problem involves two small parametersϵandμthat describe film thickness and roughness wavelength, respectively. Depending on the ratio λ=ϵ/μ, three different flow regimes are obtained in the limit as both of them tend to zero. Time-dependent equations of Reynolds type are obtained in all three cases (Stokes roughness, Reynolds roughness and high-frequency roughness regime). The derivations of the limiting equations are based on formal expansions in the parametersϵandμ.
authors.affiliation: Department of Engineering Sciences and Mathematics , Luleå University of Technology , Luleå 971 87, Sweden.
authors.forename: J
authors.initials: J
authors.lastname: Fabricius
authors.affiliation: Department of Engineering Sciences and Mathematics , Luleå University of Technology , Luleå 971 87, Sweden ; Faculty of Mechanics and Mathematics, Department of Differential Equations , Moscow Lomonosov State University , Moscow 119991, Russia.
authors.forename: Y O
authors.initials: YO
authors.lastname: Koroleva
authors.affiliation: Department of Engineering Sciences and Mathematics , Luleå University of Technology , Luleå 971 87, Sweden ; Faculty of Science, Department of Computer Science and Mathematics , Eduardo Mondlane University , Maputo, Mozambique.
authors.forename: A
authors.initials: A
authors.lastname: Tsandzana
authors.affiliation: Department of Engineering Sciences and Mathematics , Luleå University of Technology , Luleå 971 87, Sweden.
authors.forename: P
authors.initials: P
authors.lastname: Wall
keywords: Reynolds equation; homogenization theory; lubrication theory; surface roughness