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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.
DOI:
https://doi.org/10.4213/sm8226
 Full text:
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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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Linking options:
http://mi.mathnet.ru/eng/msb8226https://doi.org/10.4213/sm8226 http://mi.mathnet.ru/eng/msb/v205/i2/p131
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Addendum
This publication is cited in the following articles:
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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
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