A rigorous derivation of the time-dependent Reynolds equation

Article type: Research Article

Authors: Fabricius, John^; | Koroleva, Yulia^; | Wall, Peter

Affiliations: Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden | Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Moscow 119991, Russia

Note: [] Corresponding author. E-mail: [email protected]

Abstract: We study the asymptotic behavior of solutions of the evolution Stokes equation in a thin three-dimensional domain bounded by two moving surfaces in the limit as the distance between the surfaces approaches zero. Using only a priori estimates and compactness it is rigorously verified that the limit velocity field and pressure are governed by the time-dependent Reynolds equation.

Keywords: lubrication theory, thin film, asymptotic behavior, evolution Stokes equation, time-dependent Reynolds equation

DOI: 10.3233/ASY-131165

Journal: Asymptotic Analysis, vol. 84, no. 1-2, pp. 103-121, 2013