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 Trudy Inst. Mat. i Mekh. UrO RAN, 2013, Volume 19, Number 4, Pages 119–124 (Mi timm1005)

Asymptotics of a generalized solution of the stationary Navier-Stokes system on a manifold diffeomorphic to a sphere

S. V. Zakharov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: A stationary system of Navier-Stokes equations is considered on a Riemannian manifold diffeomorphic to a two-dimensional sphere. This problem can be used as a model for meteorological processes in planetary atmospheres. An asymptotic series in the viscosity parameter is constructed for a generalized solution under a constraint on the Reynolds number that guarantees the existence and uniqueness of the solution. We prove that partial sums of the series approximate the exact solution in a norm equivalent to the norm of the Sobolev space.

Keywords: Navier–Stokes system, generalized solution, Riemannian manifold.

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Document Type: Article
UDC: 517.95

Citation: S. V. Zakharov, “Asymptotics of a generalized solution of the stationary Navier-Stokes system on a manifold diffeomorphic to a sphere”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 4, 2013, 119–124

Citation in format AMSBIB
\Bibitem{Zak13} \by S.~V.~Zakharov \paper Asymptotics of a generalized solution of the stationary Navier-Stokes system on a manifold diffeomorphic to a sphere \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2013 \vol 19 \issue 4 \pages 119--124 \mathnet{http://mi.mathnet.ru/timm1005} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3364369} \elib{http://elibrary.ru/item.asp?id=20640501} 

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This publication is cited in the following articles:
1. S. V. Zakharov, “Obosnovanie asimptotik reshenii sistemy Nave–Stoksa pri malykh chislakh Reinoldsa”, Tr. IMM UrO RAN, 20, no. 2, 2014, 161–167
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