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Russian Mathematical Surveys, 2018, Volume 73, Issue 4, Pages 661–724
DOI: https://doi.org/10.1070/RM9822 (Mi rm9822) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Liouville-type theorems for the Navier–Stokes equations

G. A. Sereginab, T. N. Shilkinab

a St. Petersburg Department of the Steklov Mathematical Institute
b Voronezh State University
English version PDF (924 kB) Citations (16)
References:
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DOI: https://doi.org/10.1070/RM9822
Abstract: An approach to the study of local regularity of weak solutions of the Navier–Stokes equations is described which is based on the reduction of questions of local smoothness of the original solutions to the proof of Liouville-type theorems for bounded ancient solutions of it. A survey is also given of results on Liouville theorems that are known at present for various classes of ancient solutions of the Navier–Stokes equations.
Bibliography: 55 titles.
Keywords: Navier–Stokes equations, ancient solutions, Liouville theorems.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.Z50.31.0037
This research was carried out with the financial support of the Ministry of Education and Science of the Russian Federation (project no. 14.Z50.31.0037).
Received: 26.03.2018
Russian version:
Uspekhi Matematicheskikh Nauk, 2018, Volume 73, Issue 4(442), Pages 103–170
DOI: https://doi.org/10.4213/rm9822
Bibliographic databases:
Document Type: Article
UDC: 517.958:531.32
MSC: Primary 35B53, 35Q30; Secondary 35D30
Language: English
Original paper language: Russian
Citation: G. A. Seregin, T. N. Shilkin, “Liouville-type theorems for the Navier–Stokes equations”, Uspekhi Mat. Nauk, 73:4(442) (2018), 103–170; Russian Math. Surveys, 73:4 (2018), 661–724
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
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    Abstract page:845
    Russian version PDF:193
    English version PDF:33
    References:100
    First page:72
     
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