ASYMPTOTIC ANALYSIS AND PARTIAL ASYMPTOTIC DECOMPOSITION OF DOMAIN FOR STOKES EQUATION IN TUBE STRUCTURE

Abstract

The Stokes problem posed in tube structures (or finite rod structures (see Panasenko10)), i.e. in connected finite unions of the thin cylinders with the ratio of the diameter to the height of the order [Formula: see text], 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 was considered by Nazarov.8 The method of asymptotic partial decomposition of the domain (MAPDD) (see Panasenko11) is applied and justified for the Stokes problem posed in a tube structures. This method reduces the initial Stokes problem to the Stokes problem in some small parts of the domain (where the boundary layers are "concentrated".)