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Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 2, Pages 161–167 (Mi timm1067)  

Justification of the asymptotics of solutions of the Navier–Stokes system for low Reynolds numbers

S. V. Zakharov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: 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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Bibliographic databases:

Document Type: Article
UDC: 517.95
Received: 10.02.2014

Citation: S. V. Zakharov, “Justification of the asymptotics of solutions of the Navier–Stokes system for low Reynolds numbers”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 2, 2014, 161–167

Citation in format AMSBIB
\Bibitem{Zak14}
\by S.~V.~Zakharov
\paper Justification of the asymptotics of solutions of the Navier--Stokes system for low Reynolds numbers
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2014
\vol 20
\issue 2
\pages 161--167
\mathnet{http://mi.mathnet.ru/timm1067}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3364148}
\elib{http://elibrary.ru/item.asp?id=21585633}


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