TY - JOUR

T1 - Asymptotic analysis of the Navier-Stokes system in a plane domain with thin channels

AU - Maz'ya, V. G.

AU - Slutskiǐ, A. S.

PY - 2000/5/1

Y1 - 2000/5/1

N2 - A flow of viscous incompressible fluid in a domain Ωεdepending on a small parameter ε is considered. The domain Ωε is the union of a domain Ω0 with piecewise smooth baundary and thin channels with width of order ε. Every channel contains one angle point of the domain Ω0 near the channel's inlet. We prove the existence of a solution (vε, pε) to the Navier-Stokes system such that in a neighbourhood of an angle point of the domain Ω0 the pair (vε, pε) 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 (vε, pε) asymptotically coincides with the Poiseuille solution. Asymptotic expressions for the kinetic energy and the Dirichlet integral of (vε, pε) are obtained.

AB - A flow of viscous incompressible fluid in a domain Ωεdepending on a small parameter ε is considered. The domain Ωε is the union of a domain Ω0 with piecewise smooth baundary and thin channels with width of order ε. Every channel contains one angle point of the domain Ω0 near the channel's inlet. We prove the existence of a solution (vε, pε) to the Navier-Stokes system such that in a neighbourhood of an angle point of the domain Ω0 the pair (vε, pε) 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 (vε, pε) asymptotically coincides with the Poiseuille solution. Asymptotic expressions for the kinetic energy and the Dirichlet integral of (vε, pε) are obtained.

UR - http://www.scopus.com/inward/record.url?scp=0042725906&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0042725906

VL - 23

SP - 59

EP - 89

JO - Asymptotic Analysis

JF - Asymptotic Analysis

SN - 0921-7134

IS - 1

ER -