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

Authors :
Cardone, G.
Fares, R.
Panasenko, G. P.
Source :
Journal of Mathematical Physics 53, 2012, n. 10, 103702, 21 pp
Publication Year :
2012

Abstract

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.<br />Comment: 22 pages, 20 figures

Details

Database :
arXiv
Journal :
Journal of Mathematical Physics 53, 2012, n. 10, 103702, 21 pp
Publication Type :
Report
Accession number :
edsarx.1201.2121
Document Type :
Working Paper
Full Text :
https://doi.org/10.1063/1.4746738