Abstract:
The behaviour as t→∞ 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.
Citation:
N. A. Khisamutdinova, “Stabilization of the solution of a two-dimensional system of Navier–Stokes
equations in an unbounded domain with several exits to infinity”, Sb. Math., 194:3 (2003), 391–422
\Bibitem{Khi03}
\by N.~A.~Khisamutdinova
\paper Stabilization of the~solution of a~two-dimensional system of Navier--Stokes
equations in an~unbounded domain with several exits to infinity
\jour Sb. Math.
\yr 2003
\vol 194
\issue 3
\pages 391--422
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\crossref{https://doi.org/10.1070/SM2003v194n03ABEH000722}
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Linking options:
https://www.mathnet.ru/eng/sm722
https://doi.org/10.1070/SM2003v194n03ABEH000722
https://www.mathnet.ru/eng/sm/v194/i3/p83
This publication is cited in the following 1 articles:
L. M. Kozhevnikova, “Stabilization of a solution of the first mixed problem for a quasi-elliptic evolution equation”, Sb. Math., 196:7 (2005), 999–1032
Citation in format AMSBIB
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