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Zap. Nauchn. Sem. POMI, 2006, Volume 336, Pages 199–210 (Mi znsl202)  

This article is cited in 10 scientific papers (total in 10 papers)

Estimates of suitable weak solutions to the Navier–Stokes equations in critical Morrey spaces

G. A. Seregin

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: We prove some estimates for suitable weak solutions to the nonstationary three-dimensional Navier–Stokes equations under assumptions that certain invariant functionals of the velocity field are bounded.

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English version:
Journal of Mathematical Sciences (New York), 2007, 143:2, 2961–2968

Bibliographic databases:

UDC: 517
Received: 25.01.2006
Language:

Citation: G. A. Seregin, “Estimates of suitable weak solutions to the Navier–Stokes equations in critical Morrey spaces”, Boundary-value problems of mathematical physics and related problems of function theory. Part 37, Zap. Nauchn. Sem. POMI, 336, POMI, St. Petersburg, 2006, 199–210; J. Math. Sci. (N. Y.), 143:2 (2007), 2961–2968

Citation in format AMSBIB
\Bibitem{Ser06}
\by G.~A.~Seregin
\paper Estimates of suitable weak solutions to the Navier--Stokes equations in critical Morrey spaces
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~37
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 336
\pages 199--210
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl202}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2270885}
\zmath{https://zbmath.org/?q=an:1127.35042}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 143
\issue 2
\pages 2961--2968
\crossref{https://doi.org/10.1007/s10958-007-0178-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34247548774}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. A. Seregin, “Local regularity for suitable weak solutions of the Navier–Stokes equations”, Russian Math. Surveys, 62:3 (2007), 595–614  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Seregin G., Zajaczkowski W., “A sufficient condition of regularity for axially symmetric solutions to the Navier–Stokes equations”, SIAM J Math Anal, 39:2 (2007), 669–685  crossref  mathscinet  zmath  isi  elib  scopus
    3. J. Math. Sci. (N. Y.), 166:1 (2010), 1–10  mathnet  crossref
    4. Seregin G., Sverak V., “On Type I Singularities of the Local Axi-Symmetric Solutions of the Navier–Stokes Equations”, Comm Partial Differential Equations, 34:2 (2009), 171–201  crossref  mathscinet  zmath  isi  elib  scopus
    5. J. Math. Sci. (N. Y.), 166:1 (2010), 40–52  mathnet  crossref
    6. J. Math. Sci. (N. Y.), 178:3 (2011), 282–291  mathnet  crossref
    7. Wang W.D., “Non Blow-Up Criterion For the 3-D Magneto-Hydrodynamics Equations in the Limiting Case”, Acta. Math. Sin.-English Ser., 33:7 (2017), 969–980  crossref  mathscinet  zmath  isi  scopus
    8. 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
    9. Schonbek M., Seregin G., “Time Decay For Solutions to the Stokes Equations With Drift”, Commun. Contemp. Math., 20:3 (2018), 1750046  crossref  mathscinet  zmath  isi  scopus
    10. G. Seregin, “A note on weak solutions to the Navier–Stokes equations that are locally in $L_\infty(L^{3,\infty})$”, Algebra i analiz, 32:3 (2020), 238–253  mathnet
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