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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] Marchuk G. I., Dymnikov V. P., Zalesnyi V. B., Matematicheskie modeli v geofizicheskoi gidrodinamike i chislennye metody ikh realizatsii, Gidrometeoizdat, L., 1987, 287 pp.

[2] Ilin A. A., “Uravneniya Nave–Stoksa i Eilera na dvumernykh zamknutykh mnogoobraziyakh”, Mat. sb., 181:4 (1990), 521–539 | Zbl

[3] Ladyzhenskaya O. A., Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, GIFML, M., 1961, 204 pp.

[4] Zakharov S. V., “Regulyarnaya asimptotika obobschennogo resheniya statsionarnoi sistemy Nave–Stoksa”, Tr. In-ta matematiki i mekhaniki UrO RAN, 18, no. 2, 2012, 108–113

[5] Gilbarg D., Trudinger N. S., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989, 464 pp.