Geodesic
Stabilization of the~solution of a~two-dimensional system of Navier--Stokes
Sbornik. Mathematics, Tome 194 (2003) no. 3, pp. 391-422

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The behaviour as $t\to\infty$ of the solution of the mixed problem for the system of Navier–Stokes equations with a Dirichlet condition at the boundary is studied in an unbounded two-dimensional domain with several exits to infinity. A class of domains is distinguished in which an estimate characterizing the decay of solutions in terms of the geometry of the domain is proved for exponentially decreasing initial velocities. A similar estimate of the solution of the first mixed problem for the heat equation is sharp in a broad class of domains with several exits to infinity. 
@article{SM_2003_194_3_a4,
     author = {N. A. Khisamutdinova},
     title = {Stabilization of the~solution of a~two-dimensional system of {Navier--Stokes}},
     journal = {Sbornik. Mathematics},
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     volume = {194},
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     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_3_a4/}
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N. A. Khisamutdinova. Stabilization of the~solution of a~two-dimensional system of Navier--Stokes. Sbornik. Mathematics, Tome 194 (2003) no. 3, pp. 391-422. http://geodesic.mathdoc.fr/item/SM_2003_194_3_a4/