Justification of lubrication approximation: An application to fluid/solid interactions

Article type: Research Article

Authors: Hillairet, M.^{a; *} | Kelaï, T.^b

Affiliations: [a] IMAG, Université de Montpellier, Montpellier, France | [b] IMJ-PRG et Université Paris 7, Paris, France

Correspondence: [*] Corresponding author: M. Hillairet, IMAG, Université de Montpellier, Place Eugene Bataillon, 34095 Montpellier, France. E-mail: [email protected].

Abstract: We consider the stationary Stokes problem in a three-dimensional fluid domain F with non-homogeneous Dirichlet boundary conditions. We assume that this fluid domain is the complement of a bounded obstacle B in a bounded or an exterior smooth container Ω. We compute sharp asymptotics of the solution to the Stokes problem when the distance between the obstacle and the container boundary is small.

Keywords: fluid/solid interactions, Stokes problem, lubrication approximation

DOI: 10.3233/ASY-151319

Journal: Asymptotic Analysis, vol. 95, no. 3-4, pp. 187-241, 2015