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Mat. Sb., 2014, Volume 205, Number 2, Pages 131–144 (Mi msb8226)  

This article is cited in 1 scientific paper (total in 1 paper)

Smooth solutions of the Navier-Stokes equations

S. I. Pokhozhaev

Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: We consider smooth solutions of the Cauchy problem for the Navier-Stokes equations on the scale of smooth functions which are periodic with respect to $x\in\mathbb R^3$.
We obtain existence theorems for global (with respect to $t>0$) and local solutions of the Cauchy problem. The statements of these depend on the smoothness and the norm of the initial vector function. Upper bounds for the behaviour of solutions in both classes, which depend on $t$, are also obtained.
Bibliography: 10 titles.

Keywords: Navier-Stokes equations, smooth (strong) solutions, bounds for solutions.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00348-а
11-01-12018-офи-м
Ministry of Education and Science of the Russian Federation 8215


DOI: https://doi.org/10.4213/sm8226

Full text: PDF file (489 kB)
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English version:
Sbornik: Mathematics, 2014, 205:2, 277–290

Bibliographic databases:

UDC: 517.954
MSC: 76D05
Received: 25.02.2013 and 13.06.2013

Citation: S. I. Pokhozhaev, “Smooth solutions of the Navier-Stokes equations”, Mat. Sb., 205:2 (2014), 131–144; Sb. Math., 205:2 (2014), 277–290

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb/v205/i2/p131

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    Addendum

    This publication is cited in the following articles:
    1. A. A. Ilyin, “A class of sharp inequalities for periodic functions. Addendum to the paper “Smooth solutions of the Navier-Stokes equations” by S. I. Pokhozhaev”, Sb. Math., 205:2 (2014), 220–223  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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