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Zapiski Nauchnykh Seminarov POMI, 2004, Volume 310, Pages 158–190 (Mi znsl811)  
This article is cited in 26 scientific papers (total in 26 papers)

Boundary partial regularity for the Navier–Stokes equations

G. A. Seregin, T. N. Shilkin, V. A. Solonnikov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (318 kB) Citations (26)
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Abstract: We prove two conditions of local Hölder continuity for suitable weak solutions to the Navier–Stokes equations near the smooth curved part of the boundary of a domain. One of these condition has the form of the Caffarelli–Kohn–Nirenberg condition for the local boundedness of suitable weak solutions at the interior points of the space-time cylinder. The corresponding results near the plane part of the boundary were established earlier by G. Seregin.
Received: 15.10.2004
English version:
Journal of Mathematical Sciences (New York), 2006, Volume 132, Issue 3, Pages 339–358
DOI: https://doi.org/10.1007/s10958-005-0502-7
Bibliographic databases:
UDC: 517
Language: English
Citation: G. A. Seregin, T. N. Shilkin, V. A. Solonnikov, “Boundary partial regularity for the Navier–Stokes equations”, Boundary-value problems of mathematical physics and related problems of function theory. Part 35, Zap. Nauchn. Sem. POMI, 310, POMI, St. Petersburg, 2004, 158–190; J. Math. Sci. (N. Y.), 132:3 (2006), 339–358
Citation in format AMSBIB
\Bibitem{SerShiSol04}
\by G.~A.~Seregin, T.~N.~Shilkin, V.~A.~Solonnikov
\paper Boundary partial regularity for the Navier--Stokes equations
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~35
\serial Zap. Nauchn. Sem. POMI
\yr 2004
\vol 310
\pages 158--190
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl811}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2120190}
\zmath{https://zbmath.org/?q=an:1095.35031}
\elib{https://elibrary.ru/item.asp?id=9128692}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 132
\issue 3
\pages 339--358
\crossref{https://doi.org/10.1007/s10958-005-0502-7}
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    • This publication is cited in the following 26 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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