The method of asymptotic partial decomposition of a domain (MAPDD) proposed and
justified earlier for thin domains (rod structures, tube structures consisting of a set of thin
cylinders) generates some special interface conditions between the three-dimensional and
one-dimensional parts. In the case of fluid mechanics this method generates a variational
formulation of the velocity with Poiseuille type or Womersley type flow in the tubes at a small
distance from the ends. However, the pressure should then be reconstructed using the …

The method of asymptotic partial decomposition of thin domains was introduced in [1]. For
the Stokes or Navier-Stokes equations in thin tube structures it is presented in [2],[3],[4]. This
method uses the variational formulation “without pressure” and provides a special restriction
of this formulation on the Sobolev subspace of vector-valued functions having the Poiseuille-
like shape within the thin tubes at some small distance from the bifurcations. However for its
numerical implementation a weak formulation “with pressure” is needed. The main result of …