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Sbornik: Mathematics, 2014, Volume 205, Issue 2, Pages 277–290
DOI: https://doi.org/10.1070/SM2014v205n02ABEH004375 (Mi sm8226) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Smooth solutions of the Navier-Stokes equations

S. I. Pokhozhaev

Steklov Mathematical Institute of the Russian Academy of Sciences
English version PDF (440 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM2014v205n02ABEH004375
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
Received: 25.02.2013 and 13.06.2013
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 2, Pages 131–144
DOI: https://doi.org/10.4213/sm8226
Bibliographic databases:
Document Type: Article
UDC: 517.954
MSC: 76D05
Language: English
Original paper language: Russian
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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  • https://doi.org/10.1070/SM2014v205n02ABEH004375
  • https://www.mathnet.ru/eng/sm/v205/i2/p131
    Addendum
    This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
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    References:131
    First page:84
     
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