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On asymptotic solutions of boundary-value problems in thin domains
- Publisher
- Springer Journals
- Copyright
- Copyright © 2017 by Springer Science+Business Media Dordrecht
- Subject
- Physics; Classical Mechanics; Applications of Mathematics; Analysis; Mathematical Modeling and Industrial Mathematics
- ISSN
- 0022-0833
- eISSN
- 1573-2703
- DOI
- 10.1007/s10665-017-9910-1
- Publisher site
- See Article on Publisher Site
Abstract
This article outlines a family of approximations for solutions to the incompressible Navier–Stokes equations valid for flow domains that have one small dimension. The approach is applicable to two- or three-dimensional systems, steady or unsteady flows, viscous or inviscid fluids, high or low Reynolds numbers, and internal or external domains. Among the methods in this class are lubrication theories, slender-body theories, shallow-water theories, Hele–Shaw flows, and boundary layers. By displaying the commonalities in these, one sees a systematic approach to many fluid- flow problems as well as those in other fields.
Journal
Journal of Engineering Mathematics – Springer Journals
Published: Jun 8, 2017