Geodesic
Justification of the asymptotics of solutions of the Navier–Stokes system for low Reynolds numbers
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 161-167 Cet article a éte moissonné depuis la source Math-Net.Ru

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Asymptotics of a generalized solution of the steady-state Navier–Stokes system of equations in a bounded domain $\Omega$ of the three-dimensional space is studied under constraint on the generalized Reynolds number. By methods of functional analysis a theorem about approximation of the exact solution of the homogeneous boundary value problem by partial sums of the found series up to any degree of accuracy in the norm of space $C(\overline\Omega)$ is proved. For the non-steady-state Navier–Stokes system of equations asymptotic approximation in the norm of space $L_2(\Omega)$ is proved.
Keywords: the Navier–Stokes system, asymptotic approximation. 
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S. V. Zakharov. Justification of the asymptotics of solutions of the Navier–Stokes system for low Reynolds numbers. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 161-167. http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a13/

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

[2] 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

[3] Zakharov S. V., “Asimptotika obobschennogo resheniya statsionarnoi sistemy Nave–Stoksa na mnogoobrazii, diffeomorfnom sfere”, Tr. In-ta matematiki i mekhaniki UrO RAN, 19, no. 4, 2013, 119–124

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

[5] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Izd-vo LGU, L., 1950, 255 pp. | MR