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Mat. Sb. (N.S.), 1973, Volume 91(133), Number 1(5), Pages 3–26 (Mi msb3072)  

This article is cited in 27 scientific papers (total in 28 papers)

On stationary solutions of the problem of flow past a body of a viscous incompressible fluid

K. I. Babenko


Abstract: The stationary solutions of the problem of flow past a body with finite Dirichlet integral are considered. It is found that the vector velocity $\mathbf u(\mathbf x)$ differs from its limit value $\mathbf u_\infty$ by a quantity $O(|\mathbf x|^{-1})$. By the same token it is proved that any solution of the flow problem with finite Dirichlet integral possesses a wake outside which the vorticity is exponentially small.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Sbornik, 1973, 20:1, 1–25

Bibliographic databases:

UDC: 532.516
MSC: Primary 76D05; Secondary 76D25, 35Q10, 76D10
Received: 07.09.1972

Citation: K. I. Babenko, “On stationary solutions of the problem of flow past a body of a viscous incompressible fluid”, Mat. Sb. (N.S.), 91(133):1(5) (1973), 3–26; Math. USSR-Sb., 20:1 (1973), 1–25

Citation in format AMSBIB
\Bibitem{Bab73}
\by K.~I.~Babenko
\paper On~stationary solutions of the problem of flow past a~body of a~viscous incompressible fluid
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 91(133)
\issue 1(5)
\pages 3--26
\mathnet{http://mi.mathnet.ru/msb3072}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=348301}
\zmath{https://zbmath.org/?q=an:0285.76009}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 20
\issue 1
\pages 1--25
\crossref{https://doi.org/10.1070/SM1973v020n01ABEH001823}


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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. H. F. Weinberger, D. Gilbarg, “Asymptotic properties of Leray's solution of the stationary two-dimensional Navier–Stokes equations”, Russian Math. Surveys, 29:2 (1974), 109–123  mathnet  crossref  mathscinet  zmath
    2. John G. Heywood, “On uniqueness questions in the theory of viscous flow”, Acta Math, 136:1 (1976), 61  crossref  mathscinet  zmath
    3. Atsushi Inoue, Tadahisa Funaki, “On a new derivation of the Navier–Stokes equation”, Comm Math Phys, 65:1 (1979), 83  crossref  mathscinet  zmath
    4. L. R. Volevich, G. P. Voskresenskii, A. V. Zabrodin, A. N. Kolmogorov, O. A. Oleinik, V. M. Tikhomirov, “Konstantin Ivanovich Babenko (on his sixtieth birthday)”, Russian Math. Surveys, 35:2 (1980), 266–275  mathnet  crossref  mathscinet  zmath
    5. Paolo Maremonti, “Stabilità asintotica in media per moti fluidi viscosi in domini esterni”, Annali di Matematica, 142:1 (1985), 57  crossref  mathscinet  zmath  isi
    6. Nobuyoshi Tosaka, Kazuei Onishi, “Boundary integral equation formulations for steady Navier–Stokes equations using the Stokes fundamental solutions”, Engineering Analysis, 2:3 (1985), 128  crossref
    7. Wolfgang Borchers, Konstantin Pileckas, “Existence, uniqueness and asymptotics of steady jets”, Arch Rational Mech Anal, 120:1 (1992), 1  crossref  mathscinet  zmath
    8. Reinhard Farwig, “The stationary exterior 3 D-problem of Oseen and Navier–Stokes equations in anisotropically weighted Sobolev spaces”, Math Z, 211:1 (1992), 409  crossref  mathscinet  zmath  isi
    9. L. I. Sazonov, “Justification of the linearization method in the flow problem”, Russian Acad. Sci. Izv. Math., 45:2 (1995), 315–337  mathnet  crossref  mathscinet  zmath  isi
    10. L. I. Sazonov, “On the asymptotics of the solution to the three-dimensional problem of flow far from streamlined bodies”, Izv. Math., 59:5 (1995), 1051–1075  mathnet  crossref  mathscinet  zmath  isi
    11. Nazarov S., Pileckas K., “On Steady Stokes and Navier–Stokes Problems with Zero Velocity at Infinity in a Three-Dimensional Exterior Domain”, J. Math. Kyoto Univ., 40:3 (2000), 475–492  isi
    12. Ulrich Razafison, “Anisotropic weighted spaces for the stationary exterior 3D-problem of Oseen”, Journal of Mathematical Analysis and Applications, 323:1 (2006), 275  crossref
    13. Chérif Amrouche, Ulrich Razafison, “Weighted estimates for the Oseen problem in”, Applied Mathematics Letters, 19:1 (2006), 56  crossref
    14. CHÉRIF AMROUCHE, ULRICH RAZAFISON, “ON THE OSEEN PROBLEM IN THREE-DIMENSIONAL EXTERIOR DOMAINS”, Anal. Appl, 04:02 (2006), 133  crossref
    15. Giovanni P. Galdi, “Further properties of steady-state solutions to the Navier–Stokes problem past a three-dimensional obstacle”, J Math Phys (N Y ), 48:6 (2007), 065207  crossref  mathscinet  zmath  adsnasa  isi
    16. Chérif Amrouche, Huy Hoang Nguyen, “The stationary three-dimensional Navier–Stokes equations with a non-zero constant velocity at infinity”, Math Meth Appl Sci, 2008  crossref  isi
    17. Ulrich Razafison, “The stationary Navier–Stokes equations in 3D exterior domains. An approach in anisotropically weighted spaces”, Journal of Differential Equations, 245:10 (2008), 2785  crossref
    18. Giovanni P. Galdi, Mads Kyed, “Steady-State Navier–Stokes Flows Past a Rotating Body: Leray Solutions are Physically Reasonable”, Arch Rational Mech Anal, 2010  crossref
    19. L. I. Sazonov, “O suschestvovanii perekhodov mezhdu statsionarnymi rezhimami zadachi obtekaniya”, Vladikavk. matem. zhurn., 13:4 (2011), 60–69  mathnet
    20. Amrouche Ch., Bouzit H., Razafison U., “On the Two and Three Dimensional Oseen Potentials”, Potential Anal, 34:2 (2011), 163–179  crossref  isi
    21. Horst Heck, Hyunseok Kim, Hideo Kozono, “Weak solutions of the stationary Navier–Stokes equations for a viscous incompressible fluid past an obstacle”, Math. Ann, 2012  crossref
    22. Paul Deuring, “Spatial Decay of Time-Dependent Incompressible Navier–Stokes Flows with Nonzero Velocity at Infinity”, SIAM J. Math. Anal, 45:3 (2013), 1388  crossref
    23. Matthieu Hillairet, Peter Wittwer, “On the existence of solutions to the planar exterior Navier Stokes system”, Journal of Differential Equations, 2013  crossref
    24. L. I. Sazonov, “Existence of transitions between stationary regimes of the Navier–Stokes equations in the entire space”, Comput. Math. Math. Phys., 53:9 (2013), 1377–1390  mathnet  crossref  crossref  isi  elib  elib
    25. Chérif Amrouche, Mohamed Meslameni, Šárka Nečasová, “The stationary Oseen equations in an exterior domain: An approach in weighted Sobolev spaces”, Journal of Differential Equations, 2013  crossref
    26. Julien Guillod, Peter Wittwer, “Asymptotic behaviour of solutions to the stationary Navier–Stokes equations in two-dimensional exterior domains with zero velocity at infinity”, Math. Models Methods Appl. Sci, 2014, 1  crossref
    27. Paul Deuring, “Pointwise Spatial Decay of Weak Solutions to the Navier–Stokes System in 3D Exterior Domains”, J. Math. Fluid Mech, 2015  crossref
    28. Mikhail Korobkov, Konstantin Pileckas, Remigio Russo, “The Liouville Theorem for the Steady-State Navier–Stokes Problem for Axially Symmetric 3D Solutions in Absence of Swirl”, J. Math. Fluid Mech, 2015  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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