A flow of viscous incompressible fluid in a domain
$&OHgr;_ϵ$
depending on a small parameter
$ϵ$
is considered. The domain
$&OHgr;_ϵ$
is the union of a domain
$&OHgr;_0$
with piecewise smooth baundary and thin channels with width of order
$ϵ$
. Every channel contains one angle point of the domain
$&OHgr;_0$
near the channel’s inlet.
We prove the existence of a solution (v
$_ϵ,p_ϵ$
) to the Navier–Stokes system such that in a neighbourhood of an angle point of the domain
$&OHgr;_0$
the pair (v
$_ϵ,p_ϵ$
) 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
$_ϵ,p_ϵ$
) asymptotically coincides with the Poiseuille solution. Asymptotic expressions for the kinetic energy and the Dirichlet integral of (v
$_ϵ,p_ϵ$
) are obtained.
