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Asymptotic analysis of the Navier-Stokes system in a plane domain with thin channels
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden Inst Problems Mech Engn, St Petersburg 199178, Russia.
2000 (English)In: Asymptotic Analysis, ISSN 0921-7134, Vol. 23, no 1, 59-89 p.Article in journal (Refereed) Published
Abstract [en]

A flow of viscous incompressible fluid in a domain Omega(epsilon) depending on a small parameter epsilon is considered. The domain Omega(epsilon) is the union of a domain Omega(0) with piecewise smooth baundary and thin channels with width of order epsilon. Every channel contains one angle point of the domain Omega(0) near the channel's inlet. We prove the existence of a solution (v(epsilon), p(epsilon)) to the Navier-Stokes system such that in a neighbourhood of an angle point of the domain Omega(0) the pair (v(epsilon), p(epsilon)) is equal, up to a term with finite kinetic energy, to the Jeffery-Hamel solution which describes a plane viscous source (or sink) flow between the sides of the angle. In the channels the pair (v(epsilon), epsilon) asymptotically coincides with the Poiseuille solution. Asymptotic expressions for the kinetic energy and the Dirichlet integral of (v(epsilon), p(epsilon)) are obtained.

Place, publisher, year, edition, pages
2000. Vol. 23, no 1, 59-89 p.
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-49773OAI: diva2:270669
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2011-01-14

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Maz´ya, Vladimir G.
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