Geodesic
Asymptotics of a generalized solution of the stationary Navier-Stokes system on a manifold diffeomorphic to a sphere
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 4, pp. 119-124

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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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     author = {S. V. Zakharov},
     title = {Asymptotics of a generalized solution of the stationary {Navier-Stokes} system on a manifold diffeomorphic to a sphere},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_4_a11/}
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S. V. Zakharov. Asymptotics of a generalized solution of the stationary Navier-Stokes system on a manifold diffeomorphic to a sphere. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 4, pp. 119-124. http://geodesic.mathdoc.fr/item/TIMM_2013_19_4_a11/