This article is cited in 1 paper

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.

UDC: 517.95

Received: 15.05.2013

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