Asymptotic expansion of the solution of the steady Stokes equation with variable viscosity in a two-dimensional tube structure

Details Asymptotic expansion of the solution of the steady Stokes equation with variable viscosity in a two-dimensional tube structure Asymptotic expansion of the solution of the steady Stokes equation with variable viscosity in a two-dimensional tube structure

2012-01-10

arxiv.org/abs/1201.2121v1

Mathematics

Analysis of PDEs

22 pages, 20 figures

Scientific paper

The Stokes equation with the varying viscosity is considered in a thin tube structure, i.e. in a connected union of thin rectangles with heights of order $\varepsilon<<1 $ and with bases of order 1 with smoothened boundary. An asymptotic expansion of the solution is constructed: it contains some Poiseuille type flows in the channels (rectangles) with some boundary layers correctors in the neighborhoods of the bifurcations of the channels. The estimates for the difference of the exact solution and its asymptotic approximation are proved.

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