Geodesic
Asymptotics as $|x|\to\infty$ of functions lying on an attractor of the two-dimensional Navier--Stokes system in an unbounded plane domian
Sbornik. Mathematics, Tome 74 (1993) no. 2, pp. 427-453

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The Navier–Stokes system is considered in a plane domain that has several exits to infinity having the form of channels of bounded width. It is assumed that the external force decays sufficiently fast at infinity. Solutions are considered that are defined and bounded for all $t\in\mathbf R$. Such solutions lie on an attractor of the system. An asymptotic expansion as $|x|\to\infty$ is obtained for these solutions. The presence of this expansion indicates, in particular, that turbulence in this situation does not propagate to infinity. 
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     author = {A. V. Babin},
     title = {Asymptotics as $|x|\to\infty$ of functions lying on an attractor of the two-dimensional {Navier--Stokes} system in an unbounded plane domian},
     journal = {Sbornik. Mathematics},
     pages = {427--453},
     publisher = {mathdoc},
     volume = {74},
     number = {2},
     year = {1993},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1993_74_2_a8/}
}
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A. V. Babin. Asymptotics as $|x|\to\infty$ of functions lying on an attractor of the two-dimensional Navier--Stokes system in an unbounded plane domian. Sbornik. Mathematics, Tome 74 (1993) no. 2, pp. 427-453. http://geodesic.mathdoc.fr/item/SM_1993_74_2_a8/