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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 397, Pages 150–156 (Mi znsl4672)  
This article is cited in 5 scientific papers (total in 5 papers)

Note on bounded scale-invariant quantities for the Navier–Stokes equations

G. Sereginab

a St. Petersburg Department of Steklov Mathematical Institute, St. Peterburg, Russia
b Center for Nonlinear PDE's, Mathematical Institute, University of Oxford, UK
Full-text PDF (196 kB) Citations (5)
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Abstract: In this note, we show that if the velocity field $v\in L_\infty(BMO^{-1})$, then all scaled energy quantities are bounded. An interesting consequence is that each axially symmetric solution to the Navier–Stokes belonging to $L_\infty(BMO^{-1})$ is smooth.
Key words and phrases: Navier–Stokes equations, bounded mean oscillations, regularity, axial symmetry, scaled energy quantities.
Received: 20.09.2011
English version:
Journal of Mathematical Sciences (New York), 2012, Volume 185, Issue 5, Pages 742–745
DOI: https://doi.org/10.1007/s10958-012-0957-2
Bibliographic databases:
Document Type: Article
UDC: 517
Language: English
Citation: G. Seregin, “Note on bounded scale-invariant quantities for the Navier–Stokes equations”, Boundary-value problems of mathematical physics and related problems of function theory. Part 42, Zap. Nauchn. Sem. POMI, 397, POMI, St. Petersburg, 2011, 150–156; J. Math. Sci. (N. Y.), 185:5 (2012), 742–745
Citation in format AMSBIB
\Bibitem{Ser11}
\by G.~Seregin
\paper Note on bounded scale-invariant quantities for the Navier--Stokes equations
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~42
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 397
\pages 150--156
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4672}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2870113}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 185
\issue 5
\pages 742--745
\crossref{https://doi.org/10.1007/s10958-012-0957-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866935811}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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