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Uspekhi Mat. Nauk, 2018, Volume 73, Issue 4(442), Pages 103–170 (Mi umn9822)  

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

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

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).


DOI: https://doi.org/10.4213/rm9822

Full text: PDF file (1016 kB)
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English version:
Russian Mathematical Surveys, 2018, 73:4, 661–724

Bibliographic databases:

Document Type: Article
UDC: 517.958:531.32
MSC: Primary 35B53, 35Q30; Secondary 35D30
Received: 26.03.2018

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 articles:
    1. M. Chernobay, “On type I blow up for the Navier–Stokes equations near the boundary”, Kraevye zadachi matematicheskoi fiziki i smezhnye voprosy teorii funktsii. 47, K 85-letiyu Vsevoloda Alekseevicha SOLONNIKOVA, Zap. nauchn. sem. POMI, 477, POMI, SPb., 2018, 136–149  mathnet
  • Успехи математических наук Russian Mathematical Surveys
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