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Eurasian Math. J., 2012, Volume 3, Number 3, Pages 62–93 (Mi emj96)  

This article is cited in 13 scientific papers (total in 13 papers)

The role of Morrey spaces in the study of Navier–Stokes and Euler equations

P.-G. Lemarié-Rieusset

Laboratoire Analyse et Probabilités, Université d'Evry, IBGBI, Evry cedex, France

Abstract: In this survey, we will pay a few words on the solution of the Cauchy problem for the 3D Navier–Stokes or Euler equations (with a focus on real harmonic analysis methods). Then we will highlight the role of Morrey spaces in other problems for the Navier–Stokes equations : uniqueness, weak-strong uniqueness, self-similar solutions, etc.

Keywords and phrases: Morrey spaces, Euler equations, Navier–Stokes equations, Cauchy problem.

Full text: PDF file (554 kB)
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Bibliographic databases:
MSC: 46E30, 35Q30
Received: 20.02.2012
Language:

Citation: P.-G. Lemarié-Rieusset, “The role of Morrey spaces in the study of Navier–Stokes and Euler equations”, Eurasian Math. J., 3:3 (2012), 62–93

Citation in format AMSBIB
\Bibitem{Lem12}
\by P.-G.~Lemari\'e-Rieusset
\paper The role of Morrey spaces in the study of Navier--Stokes and Euler equations
\jour Eurasian Math. J.
\yr 2012
\vol 3
\issue 3
\pages 62--93
\mathnet{http://mi.mathnet.ru/emj96}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3024130}
\zmath{https://zbmath.org/?q=an:1277.46017}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. I. Burenkov, “Recent progress in studying the boundedness of classical operators of real analysis in general Morrey-type spaces. I”, Eurasian Math. J., 3:3 (2012), 11–32  mathnet  mathscinet  zmath
    2. V. I. Burenkov, “Recent progress in studying the boundedness of classical operators of real analysis in general Morrey-type spaces. II”, Eurasian Math. J., 4:1 (2013), 21–45  mathnet  mathscinet  zmath
    3. V. I. Burenkov, D. K. Darbayeva, E. D. Nursultanov, “Description of interpolation spaces for general local Morrey-type spaces”, Eurasian Math. J., 4:1 (2013), 46–53  mathnet  mathscinet  zmath
    4. T. V. Tararykova, “Comments on definitions of general local and global Morrey-type spaces”, Eurasian Math. J., 4:1 (2013), 125–134  mathnet  mathscinet  zmath
    5. Triebel H., “Local Function Spaces, Heat and Navier-Stokes Equations”, Local Function Spaces, Heat and Navier-Stokes Equations, Ems Tracts in Mathematics, 20, Eur. Math. Soc., 2013, 1–232  crossref  mathscinet  zmath  isi
    6. V. I. Burenkov, E. D. Nursultanov, D. K. Chigambayeva, “Description of the interpolation spaces for a pair of local Morrey-type spaces and their generalizations”, Proc. Steklov Inst. Math., 284 (2014), 97–128  mathnet  crossref  crossref  isi  elib  elib
    7. Triebel H., “Hybrid Function Spaces, Heat and Navier-Stokes Equations”, Hybrid Function Spaces, Heat and Navier-Stokes Equations, Ems Tracts in Mathematics, 24, Eur. Math. Soc., 2014, 1–185  mathscinet  isi
    8. Yuan Wen, Winfried S., Yang DaChun, “Interpolation of Morrey-Campanato and Related Smoothness Spaces”, Sci. China-Math., 58:9 (2015), 1835–1908  crossref  mathscinet  zmath  isi  scopus
    9. V. I. Burenkov, T. V. Tararykova, “An analog of Young's inequality for convolutions of functions for general Morrey-type spaces”, Proc. Steklov Inst. Math., 293 (2016), 107–126  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    10. V. I. Burenkov, T. V. Tararykova, “Young’s inequality for convolutions in Morrey-type spaces”, Eurasian Math. J., 7:2 (2016), 92–99  mathnet
    11. Haroske D.D., Schneider C., Skrzypczak L., “Morrey Spaces on Domains: Different Approaches and Growth Envelopes”, J. Geom. Anal., 28:2 (2018), 817–841  crossref  mathscinet  zmath  isi  scopus
    12. V. I. Burenkov, D. K. Chigambayeva, E. D. Nursultanov, “Marcinkiewicz-type interpolation theorem and estimates for convolutions for Morrey-type spaces”, Eurasian Math. J., 9:2 (2018), 82–88  mathnet  mathscinet  isi
    13. N. R. Ahmedzade, Z. A. Kasumov, “On the Dirichlet problem for the Laplace equation with the boundary value in Morrey space”, Eurasian Math. J., 9:4 (2018), 9–21  mathnet  crossref
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