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 Mat. Sb., 2002, Volume 193, Number 12, Pages 69–104 (Mi msb700)

This article is cited in 8 scientific papers (total in 8 papers)

Asymptotics of solutions of the stationary Navier–Stokes system of equations in a domain of layer type

K. Pileckas

Institute of Mathematics and Informatics

Abstract: The stationary Navier–Stokes system of equations is considered in a domain $\Omega \subset\mathbb R^3$ coinciding for large $|x|$ with the layer $\Pi =\mathbb R^2\times (0,1)$. A theorem is proved about the asymptotic behaviour of the solutions as $|x|\to\infty$. In particular, it is proved that for arbitrary data of the problem the solutions having non-zero flux through a cylindrical cross-section of the layer behave at infinity like the solutions of the linear Stokes system.

DOI: https://doi.org/10.4213/sm700

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English version:
Sbornik: Mathematics, 2002, 193:12, 1801–1836

Bibliographic databases:

UDC: 517.9
MSC: Primary 35Q30, 35B40; Secondary 35A05, 46E35, 76D05
Received: 10.08.2000 and 11.03.2002

Citation: K. Pileckas, “Asymptotics of solutions of the stationary Navier–Stokes system of equations in a domain of layer type”, Mat. Sb., 193:12 (2002), 69–104; Sb. Math., 193:12 (2002), 1801–1836

Citation in format AMSBIB
\Bibitem{Pil02} \by K.~Pileckas \paper Asymptotics of solutions of the stationary Navier--Stokes system of equations in a~domain of layer type \jour Mat. Sb. \yr 2002 \vol 193 \issue 12 \pages 69--104 \mathnet{http://mi.mathnet.ru/msb700} \crossref{https://doi.org/10.4213/sm700} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1992105} \zmath{https://zbmath.org/?q=an:1069.35052} \transl \jour Sb. Math. \yr 2002 \vol 193 \issue 12 \pages 1801--1836 \crossref{https://doi.org/10.1070/SM2002v193n12ABEH000700} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000181721200010} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0036875429} 

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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. J. Math. Sci. (N. Y.), 130:4 (2005), 4852–4870
2. V. Keblikas, K. Pileckas, “Existence of a nonstationary Poiseuille solution”, Siberian Math. J., 46:3 (2005), 514–526
3. Pileckas K., Zaleskis L., “Weighted coercive estimates of solutions to the Stokes problem in parabolically growing layer”, Asymptot. Anal., 54:3-4 (2007), 211–233
4. Chipot M., Mardare S., “Asymptotic behaviour of the Stokes problem in cylinders becoming unbounded in one direction”, J. Math. Pures Appl. (9), 90:2 (2008), 133–159
5. Nazarov S.A., Specovius-Neugebauer M., “Artificial boundary conditions for the Stokes and Navier–Stokes equations in domains that are layer-like at infinity”, Z. Anal. Anwend., 27:2 (2008), 125–155
6. Pileckas K., Specovius-Neugebauer M., “Asymptotics of solutions to the Navier–Stokes system with nonzero flux in a layer-like domain”, Asymptotic Analysis, 69:3–4 (2010), 219–231
7. K. Kaulakytė, K. Pileckas, “On the Nonhomogeneous Boundary Value Problem for the Navier–Stokes System in a Class of Unbounded Domains”, J. Math. Fluid Mech, 2012
8. Pileckas K., Specovius-Neugebauer M., “Spatial Behavior of Solutions to the Time Periodic Stokes System in a Three Dimensional Layer”, J. Differ. Equ., 263:10 (2017), 6317–6346
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