Geodesic
Asymptotics of solutions of the stationary Navier--Stokes system of equations in a~domain of layer type
Sbornik. Mathematics, Tome 193 (2002) no. 12, pp. 1801-1836

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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. 
@article{SM_2002_193_12_a3,
     author = {K. Pileckas},
     title = {Asymptotics of solutions of the stationary {Navier--Stokes} system of equations in a~domain of layer type},
     journal = {Sbornik. Mathematics},
     pages = {1801--1836},
     publisher = {mathdoc},
     volume = {193},
     number = {12},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2002_193_12_a3/}
}
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K. Pileckas. Asymptotics of solutions of the stationary Navier--Stokes system of equations in a~domain of layer type. Sbornik. Mathematics, Tome 193 (2002) no. 12, pp. 1801-1836. http://geodesic.mathdoc.fr/item/SM_2002_193_12_a3/