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Zap. Nauchn. Sem. POMI, 2004, Volume 310, Pages 158–190 (Mi znsl811)  

This article is cited in 18 scientific papers (total in 18 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

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.

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English version:
Journal of Mathematical Sciences (New York), 2006, 132:3, 339–358

Bibliographic databases:

UDC: 517
Received: 15.10.2004
Language:

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://www.ams.org/mathscinet-getitem?mr=2120190}
\zmath{https://zbmath.org/?q=an:1095.35031}
\elib{http://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 articles:
    1. J. Math. Sci. (N. Y.), 143:2 (2007), 2924–2935  mathnet  crossref  mathscinet  zmath  elib
    2. Gustafson S., Kang K., Tsai T.-P., “Interior regularity criteria for suitable weak solutions of the Navier–Stokes equations”, Comm Math Phys, 273:1 (2007), 161–176  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Suzuki T., “On partial regularity of suitable weak solutions to the Navier–Stokes equations in unbounded domains”, Manuscripta Mathematica, 125:4 (2008), 471–493  crossref  mathscinet  zmath  isi  elib  scopus
    4. J. Math. Sci. (N. Y.), 166:1 (2010), 40–52  mathnet  crossref
    5. Kim J., Kim M., “Local regularity of the Navier–Stokes equations near the curved boundary”, Journal of Mathematical Analysis and Applications, 363:1 (2010), 161–173  crossref  mathscinet  zmath  isi  scopus
    6. J. Math. Sci. (N. Y.), 178:3 (2011), 243–264  mathnet  crossref
    7. J. Math. Sci. (N. Y.), 178:3 (2011), 282–291  mathnet  crossref
    8. Lin F., Lin J., Wang Ch., “Liquid Crystal Flows in Two Dimensions”, Arch Ration Mech Anal, 197:1 (2010), 297–336  crossref  mathscinet  zmath  isi  elib  scopus
    9. Farwig R., Kozono H., Sohr H., “Regularity of Weak Solutions for the Navier–Stokes Equations Via Energy Criteria”, Advances in Mathematical Fluid Mechanics - Dedicated to Giovanni Paolo Galdi on the Occasion of His 60th Birthday, International Conference on Mathematical Fluid Mechanics, 2007, 2010, 215–227  mathscinet  zmath  isi
    10. J. Math. Sci. (N. Y.), 185:5 (2012), 659–667  mathnet  crossref  mathscinet
    11. Consiglieri L., “Partial Regularity for the Navier–Stokes-Fourier System”, Acta Math Sci Ser B Engl Ed, 31:5 (2011), 1653–1670  crossref  mathscinet  zmath  isi  scopus
    12. J. Math. Sci. (N. Y.), 195:1 (2013), 1–12  mathnet  crossref  mathscinet
    13. Vialov V., “on the Regularity of Weak Solutions To the Mhd System Near the Boundary”, J. Math. Fluid Mech., 16:4 (2014), 745–769  crossref  mathscinet  zmath  isi  elib  scopus
    14. Dong H. Gu X., “Boundary Partial Regularity For the High Dimensional Navier–Stokes Equations”, J. Funct. Anal., 267:8 (2014), 2606–2637  crossref  mathscinet  zmath  isi  elib  scopus
    15. Bae H.-O. Kang K. Kim M., “Local Regularity Criteria of the Navier–Stokes Equations With Slip Boundary Conditions”, J. Korean. Math. Soc., 53:3 (2016), 597–621  crossref  mathscinet  zmath  isi  elib  scopus
    16. Choe H.J., Jang Yu., Yang M., “Existence of Suitable Weak Solutions to the Navier–Stokes Equations in Time Varying Domains”, Nonlinear Anal.-Theory Methods Appl., 163 (2017), 163–176  crossref  mathscinet  zmath  isi  scopus
    17. J. Math. Sci. (N. Y.), 236:4 (2019), 461–475  mathnet  crossref
    18. Liu J. Wang W., “Boundary Regularity Criteria For the 6D Steady Navier–Stokes and Mhd Equations”, J. Differ. Equ., 264:3 (2018), 2351–2376  crossref  mathscinet  zmath  isi  scopus
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