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Pressure-driven flow in thin domains
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0003-1993-8229
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Department of Mathematics and Informatics, Eduardo Mondlane University, Maputo, Mozambique.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0001-8211-3671
2019 (English)In: Asymptotic Analysis, ISSN 0921-7134, E-ISSN 1875-8576Article in journal (Refereed) Epub ahead of print
Abstract [en]

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.

Place, publisher, year, edition, pages
IOS Press, 2019.
Keywords [en]
Stokes equation, pressure boundary condition, two-scale convergence, thin domain, Bogovskii operator, Korn inequality
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-75853DOI: 10.3233/ASY-191535OAI: oai:DiVA.org:ltu-75853DiVA, id: diva2:1348765
Available from: 2019-09-05 Created: 2019-09-05 Last updated: 2019-09-05

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Fabricius, JohnMiroshnikova, ElenaWall, Peter

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