Asymptotic expansion of the solution of navier-stokes equation in tube structure and partial asymptotic decomposition of the domain

Abstract

The Navier-Stokes problem stated in tube structures (or finite rod structures [4]), i.e. in connected finite unions of the thin cylinders with the ratio of the diameter to the height of the order ∊<<1, is considered. The asymptotic expansion of the solution is built and justified. Boundary layers are studied. Earlier the Navier-Stokes problem in one thin domain wa considered in [I]

The method of asymptotic partial deconiposition of the domain (MAPDD) [5],[7] is applied and justified for the Navier-Stokes problem stated in a tube structures. This method reduces the initial Navier- Stokes problem to the Navier-Stokes problem in some small parts of the domain (where the boundary layers are “concentrated.”)

The main results of the pesent article were announced in [8,9].

Stokes equation was studied in [l0, 12].

Keywords:

• Navier-Stokes
• variational formulation
• boundary layer
• asymptotic expansions

Keywords:

• 35D99
• 35B27
• 35Q30