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 Izv. RAN. Ser. Mat., 1997, Volume 61, Issue 1, Pages 113–140 (Mi izv107)

Homogenization of non-stationary Stokes equations with viscosity in a perforated domain

G. V. Sandrakov

M. V. Lomonosov Moscow State University

Abstract: Theorems are proved about the asymptotic behaviour of solutions of an initial boundary-value problem for non-stationary Stokes equations in a periodic perforated domain with a small period $\varepsilon$. The viscosity coefficient $\nu$ of the equations is assumed to be a positive parameter satisfying one of the following three conditions: $\nu/\varepsilon^2 \to \infty,1,0$ as $\varepsilon\to 0$. We also consider the case of degenerate Stokes equations with zero viscosity coefficient and the case of Navier–Stokes equations when the viscosity coefficient is not too small.

DOI: https://doi.org/10.4213/im107

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English version:
Izvestiya: Mathematics, 1997, 61:1, 113–141

Bibliographic databases:

MSC: Primary 35B27; Secondary 76D05

Citation: G. V. Sandrakov, “Homogenization of non-stationary Stokes equations with viscosity in a perforated domain”, Izv. RAN. Ser. Mat., 61:1 (1997), 113–140; Izv. Math., 61:1 (1997), 113–141

Citation in format AMSBIB
\Bibitem{San97} \by G.~V.~Sandrakov \paper Homogenization of non-stationary Stokes equations with viscosity in a~perforated domain \jour Izv. RAN. Ser. Mat. \yr 1997 \vol 61 \issue 1 \pages 113--140 \mathnet{http://mi.mathnet.ru/izv107} \crossref{https://doi.org/10.4213/im107} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1440315} \zmath{https://zbmath.org/?q=an:0893.35095} \transl \jour Izv. Math. \yr 1997 \vol 61 \issue 1 \pages 113--141 \crossref{https://doi.org/10.1070/IM1997v061n01ABEH000107} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1997XR83300005} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0039941168} 

• http://mi.mathnet.ru/eng/izv107
• https://doi.org/10.4213/im107
• http://mi.mathnet.ru/eng/izv/v61/i1/p113

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. E. Pastukhova, “Substantiation of the Darcy law for a porous medium with condition of partial adhesion”, Sb. Math., 189:12 (1998), 1871–1888
2. Sandrakov G.V., “Influence of viscosity on acoustic phenomena in porous media”, Russian Journal of Numerical Analysis and Mathematical Modelling, 13:3 (1998), 245–264
3. Pastukhova S.E., “Homogenization of the stationary Stokes system in a perforated domain with a mixed condition on the boundary of cavities”, Differential Equations, 36:5 (2000), 755–766
4. Khan K., Schwarzenberg S.J., Sharp H., Greenwood D., Weisdorf-Schindele S., “Role of serology and routine inflammatory laboratory tests in childhood bowel disease”, Inflammatory Bowel Diseases, 8:5 (2002), 325–329
5. Jason R. Looker, Steven L. Carnie, “The hydrodynamics of an oscillating porous sphere”, Phys Fluids, 16:1 (2004), 62
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7. G. V. Sandrakov, “Multiphase homogenized diffusion models for problems with several parameters”, Izv. Math., 71:6 (2007), 1193–1252
8. G. V. Sandrakov, “On some properties of solutions of Navier-Stokes equations with oscillating data”, J. Math. Sci. (N. Y.), 143:4 (2007), 3377–3385
9. Prakash J., Sekhar G.P.R., Kohr M., “Faxen's law for arbitrary oscillatory Stokes flow past a porous sphere”, Archives of Mechanics, 64:1 (2012), 41–63
10. Zhendong Luo, Fei Teng, Zhenhua Di, “A POD-based reduced-order finite difference extrapolating model with fully second-order accuracy for non-stationary Stokes equations”, International Journal of Computational Fluid Dynamics, 2014, 1
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