This article is cited in 1 scientific paper (total 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
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.
Navier–Stokes system, generalized solution, Riemannian manifold.
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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 Inst. Mat. i Mekh. UrO RAN, 19, no. 4, 2013, 119–124
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\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
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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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