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.
Citation:
K. Pileckas, “Asymptotics of solutions of the stationary Navier–Stokes system of equations in a domain of layer type”, Sb. Math., 193:12 (2002), 1801–1836
\Bibitem{Pil02}
\by K.~Pileckas
\paper Asymptotics of solutions of the stationary Navier--Stokes system of equations in a~domain of layer type
\jour Sb. Math.
\yr 2002
\vol 193
\issue 12
\pages 1801--1836
\mathnet{http://mi.mathnet.ru/eng/sm700}
\crossref{https://doi.org/10.1070/SM2002v193n12ABEH000700}
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Linking options:
https://www.mathnet.ru/eng/sm700
https://doi.org/10.1070/SM2002v193n12ABEH000700
https://www.mathnet.ru/eng/sm/v193/i12/p69
This publication is cited in the following 15 articles:
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Giovanni Leoni, Ian Tice, “Traveling Wave Solutions to the Free Boundary Incompressible Navier‐Stokes Equations”, Comm Pure Appl Math, 76:10 (2023), 2474
Stevenson N., Tice I., “Traveling Wave Solutions to the Multilayer Free Boundary Incompressible Navier-Stokes Equations”, SIAM J. Math. Anal., 53:6 (2021), 6370–6423
Tai-Peng Tsai, “Liouville type theorems for stationary Navier–Stokes equations”, SN Partial Differ. Equ. Appl., 2:1 (2021)
Kaulakyte K., Pileckas K., “Nonhomogeneous Boundary Value Problem For the Time Periodic Linearized Navier-Stokes System in a Domain With Outlet to Infinity”, J. Math. Anal. Appl., 489:1 (2020), 124126
Bryan Carrillo, Xinghong Pan, Qi S. Zhang, Na Zhao, “Decay and Vanishing of some D-Solutions of the Navier–Stokes Equations”, Arch Rational Mech Anal, 237:3 (2020), 1383
Li Z., Pan X., “On the Vanishing of Some D-Solutions to the Stationary Magnetohydrodynamics System”, J. Math. Fluid Mech., 21:4 (2019), UNSP 52
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
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
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
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
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
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
V. Keblikas, K. Pileckas, “Existence of a nonstationary Poiseuille solution”, Siberian Math. J., 46:3 (2005), 514–526
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