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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 3, pp. 302–321, March, 2009.
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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 Math J 61, 361–382 (2009). https://doi.org/10.1007/s11253-009-0219-8
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DOI: https://doi.org/10.1007/s11253-009-0219-8