The Stokes equation with the nonconstant viscosity is considered in a thin tube structure, i.e., in a connected union of thin rectangles with heights of order ε 1 and bases of order 1 with smoothened boundary. An asymptotic expansion of the solution is constructed. In the case of random perturbations of the constant viscosity, we prove that the leading term for the velocity is deterministic, while for the pressure it is random, but the expectations of the pressure satisfies the deterministic Darcy equation. Estimates for the difference between the exact solution and its asymptotic approximation are proved.

Asymptotic analysis of the steady Stokes equation with randomly perturbed viscosity in a thin tube structure / Cardone, G; Carraro, L; Fares, R; Panasenko, Gp. - In: JOURNAL OF MATHEMATICAL SCIENCES. - ISSN 1072-3374. - 176:6(2011), pp. 797-817. [10.1007/s10958-011-0437-0]

Asymptotic analysis of the steady Stokes equation with randomly perturbed viscosity in a thin tube structure

CARDONE G
;
2011

Abstract

The Stokes equation with the nonconstant viscosity is considered in a thin tube structure, i.e., in a connected union of thin rectangles with heights of order ε 1 and bases of order 1 with smoothened boundary. An asymptotic expansion of the solution is constructed. In the case of random perturbations of the constant viscosity, we prove that the leading term for the velocity is deterministic, while for the pressure it is random, but the expectations of the pressure satisfies the deterministic Darcy equation. Estimates for the difference between the exact solution and its asymptotic approximation are proved.
2011
Asymptotic analysis of the steady Stokes equation with randomly perturbed viscosity in a thin tube structure / Cardone, G; Carraro, L; Fares, R; Panasenko, Gp. - In: JOURNAL OF MATHEMATICAL SCIENCES. - ISSN 1072-3374. - 176:6(2011), pp. 797-817. [10.1007/s10958-011-0437-0]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/872218
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