Geodesic
Of the first mixed problem for the~system of Navier--Stokes equations in domains with noncompact boundaries
Sbornik. Mathematics, Tome 78 (1994) no. 2, pp. 507-524

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This article contains an investigation of the behavior as $t\to\infty$ of a solution of the mixed problem with Dirichlet conditions on the boundary for the system of Navier–Stokes equations in an unbounded three-dimensional domain. An estimate, determined by the geometry of the domain, is proved for the rate of decay of a solution for a compactly supported initial function satisfying a certain smallness condition. This estimate coincides in form with the sharp estimate obtained earlier by the author for the solution of the first mixed problem for the heat equation. 
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     author = {F. Kh. Mukminov},
     title = {Of the first mixed problem for the~system of {Navier--Stokes} equations in domains with noncompact boundaries},
     journal = {Sbornik. Mathematics},
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     url = {http://geodesic.mathdoc.fr/item/SM_1994_78_2_a13/}
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F. Kh. Mukminov. Of the first mixed problem for the~system of Navier--Stokes equations in domains with noncompact boundaries. Sbornik. Mathematics, Tome 78 (1994) no. 2, pp. 507-524. http://geodesic.mathdoc.fr/item/SM_1994_78_2_a13/