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 Mat. Sb. (N.S.), 1973, Volume 92(134), Number 4(12), Pages 589–610 (Mi msb3495)

The rate of decrease for large time of the solution of a Sobolev system with viscosity

V. N. Maslennikova

Abstract: The rate of decrease for large time, uniform with respect to $x\in E_2$, of the solution of the Cauchy problem for a linearized system governing the motion of a rotating viscous fluid is obtained for the case of two space variables. The law of decay obtained is $O(1/t^{3/2})$ for the velocity vector $\mathbf v(x,t)$ and $O(1/t)$ for the pressure function $P(x,t)$; it describes the rate of decay of the vorticity in a viscous fluid for the linear formulation considered here.
Bibliography: 8 titles.

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English version:
Mathematics of the USSR-Sbornik, 1973, 21:4, 584–606

Bibliographic databases:

UDC: 517.946.8
MSC: Primary 35B40; Secondary 35Q10, 76D05

Citation: V. N. Maslennikova, “The rate of decrease for large time of the solution of a Sobolev system with viscosity”, Mat. Sb. (N.S.), 92(134):4(12) (1973), 589–610; Math. USSR-Sb., 21:4 (1973), 584–606

Citation in format AMSBIB
\Bibitem{Mas73} \by V.~N.~Maslennikova \paper The rate of decrease for large time of the solution of a~Sobolev system with viscosity \jour Mat. Sb. (N.S.) \yr 1973 \vol 92(134) \issue 4(12) \pages 589--610 \mathnet{http://mi.mathnet.ru/msb3495} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=348303} \zmath{https://zbmath.org/?q=an:0282.35049} \transl \jour Math. USSR-Sb. \yr 1973 \vol 21 \issue 4 \pages 584--606 \crossref{https://doi.org/10.1070/SM1973v021n04ABEH002037} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Mukminov F., “Decay of the Solution of the Mixed Problem for a Linearized System of Navier–Stokes Equations”, Differ. Equ., 28:8 (1992), 1156–1164
2. F. Kh. Mukminov, “Of the first mixed problem for the system of Navier–Stokes equations in domains with noncompact boundaries”, Russian Acad. Sci. Sb. Math., 78:2 (1994), 507–524
3. N. A. Khisamutdinova, “Stabilization of the solution of a two-dimensional system of Navier–Stokes equations in an unbounded domain with several exits to infinity”, Sb. Math., 194:3 (2003), 391–422
4. Š. Nečasová, “Asymptotic properties of the steady fall of a body in viscous fluids”, Math Meth Appl Sci, 27:17 (2004), 1969
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