Affiliations: [a] Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden. E-mails: [email protected], [email protected], [email protected] | [b] Department of Mathematics and Informatics, Eduardo Mondlane University, Praça 25 de Junho, 257 C. P. 257, Maputo, Mozambique. E-mail: [email protected]
Abstract: We study the asymptotic behavior of pressure-driven Stokes flow in a thin domain. By letting the thickness of the domain tend to zero we derive a generalized form of the classical Reynolds–Poiseuille law, i.e. the limit velocity field is a linear function of the pressure gradient. By prescribing the external pressure as a normal stress condition, we recover a Dirichlet condition for the limit pressure. In contrast, a Dirichlet condition for the velocity yields a Neumann condition for the limit pressure.
