Partial asymptotic decomposition of domain: Navier-Stokes equation in tube structure

Abstract

The Navier-Stokes problem stated in tube structures (or finite rod structures), i.e. in connected finite unions of thin cylinders with ratio of the diameter to the height of the order ε < < 1, is considered. The method of asymptotic partial decomposition of the domain (MAPDD) is applied and justified for the Navier-Stokes problem posed in a tube structure. This method reduces the initial Navier-Stokes problem to the Navier-Stokes problem in certain small parts of the domain (where the boundary layers are “concentrated”).