2017
Том 69
№ 9

All Issues

Small oscillations of a viscous incompressible fluid with a large number of small interacting particles in the case of their surface distribution

Berezhnoi M. A.

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Abstract

We study the asymptotic behavior of solutions of the problem that describes small motions of a viscous incompressible fluid filling a domain Ω with a large number of suspended small solid interacting particles concentrated in a small neighborhood of a certain smooth surface Γ ⊂ Ω. We prove that, under certain conditions, the limit of these solutions satisfies the original equations in the domain Ω\Γ and some averaged boundary conditions (conjugation conditions) on Γ.

English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 3, pp 361-382.

Citation Example: Berezhnoi M. A. Small oscillations of a viscous incompressible fluid with a large number of small interacting particles in the case of their surface distribution // Ukr. Mat. Zh. - 2009. - 61, № 3. - pp. 302-321.

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