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About the Works of K. I. Babenko in the Field of Mechanics and Applied Mathematics (on the 100th Anniversary of His Birth)

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The paper provides an overview of the scientific achievements of K.I. Babenko, Corresponding Member of Academy of Sciences of the USSR, in the field of mechanics and applied mathematics, including numerical studies of ideal gas flows around a body, investigation of viscous fluid flows, and research in the field of computational mathematics. A characteristic feature of these works is the combination of deep analytical methods and tools and numerical solutions of specific problems.

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REFERENCES

  1. K. I. Babenko, “On conjugate functions,” Dokl. Akad. Nauk SSSR 62 (2), 157–160 (1948).

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  2. K. I. Babenko, V. N. Ivanova, E. P. Kazandzhan, M. A. Kukarkina, and Yu. B. Radvogin, “Unsteady Flow around the head of a blunted body by an ideal gas,” Preprint No. 72 (Keldysh Institute of Applied Mathematics, 1969).

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  3. K. I. Babenko, G. P. Voskresenskii, V. V. Rusanov, and A. N. Lyubimov, Spatial Flow around Smooth Bodies by Ideal Gas (Nauka, Moscow, 1964) [in Russian].

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  4. K. I. Babenko, N. D. Vvedenskaya, and M. M. Orlova, “On stationary viscous fluid flow past a circular cylinder,” Preprint No. 4 (Keldysh Institute of Applied Mathematics, Moscow, 1969).

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  5. K. I. Babenko, “On the asymptotic behavior of a vortex in a plane viscous fluid flow away from the body,” Prikl. Mat. Mekh. 34 (5), 911–925 (1970).

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  6. K. I. Babenko, N. D. Vvedenskaya, and M. G. Orlova, “On stationary flow of viscous fluid past a circular cylinder fluid dynamics,” Fluid Dyn. Trans. 5 (11), 37–49 (1970).

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  7. K. I. Babenko, “On the asymptotic behavior of a vortex in a plane viscous fluid flow away from the body,” Preprint No. 2 (Keldysh Institute of Applied Mathematics, Moscow, 1970).

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  8. K. I. Babenko and M. M. Vasil’ev, “Asymptotic behavior of a solution of a viscous fluid flow problem past a finite body,” Preprint No. 84 (Keldysh Institute of Applied Mathematics, Moscow, 1971).

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  9. K. I. Babenko, N. D. Vvedenskaya, and M. M. Orlova, “The results of calculation for flow around an infinite circular cylinder by a viscous fluid,” Preprint No. 38 (Keldysh Institute of Applied Mathematics, Moscow, 1971).

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  10. K. I. Babenko, N. D. Vvedenskaya, and M. M. Orlova, “Boundary value problem for Navier-Stokes equations in a plane flow problem,” Preprint No. 39 (Keldysh Institute of Applied Mathematics, Moscow, 1971).

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  11. K. I. Babenko and N. D. Vvedenskaya, “Numerical solution of the boundary value problem for the Navier-Stokes equation,” USSR Comput. Math. Math. Phys. 12 (5), 329–339 (1972).

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  12. K. I. Babenko, M. M. Vasil’ev, E. P. Kazandzhan, and M. M. Orlova, “Numerical solution of the problem on viscous incompressible fluid unsteady motion within a given region,” Preprint No. 54 (Keldysh Institute of Applied Mathematics, Moscow, 1972).

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  13. K. I. Babenko, “On stationary solutions of the problem on flow past a body of a viscous incompressible fluid,” Mat. Sb. 91 (133) (1), 3–26 (1973).

  14. K. I. Babenko and M. M. Vasil’ev, “On asymptotic behavior of stationary flow of viscous incompressible fluid far from the body,” Prikl. Mat. Mekh. 37 (4), 690–705 (1973).

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  15. K. I. Babenko, N. D. Vvedenskaya, and M. M. Orlova, “Calculation of the steady flow of a viscous fluid past a circular cylinder,” USSR Comput. Math. Math. Phys. 15 (1), 176–190 (1975).

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  16. K. I. Babenko and N. D. Vvedenskaya, “Calculation of equations and vortex at the boundary in numerical solution of the boundary value problem for Navier-Stokes equations,” in Proc. 4th All-Union Seminar on Numerical Methods of Viscous Fluid Mechanics (Novosibirsk, 1975) [in Russian].

  17. K. I. Babenko, “Perturbation theory of stationary viscous incompressible fluid flows at small Reynolds numbers,” Preprint No. 79 (Keldysh Institute of Applied Mathematics, Moscow, 1975). https://keldysh.ru/papers/1975/prep1975_79.pdf

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  18. K. I. Babenko, “Perturbation theory of stationary flows of viscous incompressible fluid for small Reynolds numbers,” Sov. Phys. Dokl. 21, 143–145 (1976).

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  19. K. I. Babenko, “On properties of steady viscous incompressible fluid flows,” in Approximation Methods for Navier-Stokes Problems (Springer, Berlin, 1980).

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  20. K. I. Babenko, “Spectrum of the linearized problem of flow of a viscous incompressible liquid around a body,” Sov. Phys. Dokl. 262 (1), 25–27 (1982).

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  21. K. I. Babenko, “Periodic solutions of the flow of a viscous fluid past a body,” Sov. Math. Dokl. 25, 211–216 (1982).

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  22. L. N. G. Filon, “The forces on a cylinder in a stream of viscous fluid,” Proc. R. Soc. London A 113, 7–27 (1926).

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  23. G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Springer Monographs in Mathematics (Springer, New York, 2011).

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  24. K. I. Babenko, “Investigation of hydrodynamic stability by means of computers,” Fluid Dyn. Trans. 10, 9–75 (1980).

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  25. K. I. Babenko and A. L. Afendikov, “On the occurrence of turbulence in viscous incompressible fluid flows,” in Mechanics and Scientific and Technical Progress (Nauka, Moscow, 1987), Vol. 2 [in Russian].

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  26. K. I. Babenko and A. I. Rakhmanov, “Proof-based calculations in the surface wave problem,” in Designing Algorithms and Solving Problems of Mathematical Physics (Keldysh Institute of Applied Mathematics, Moscow, 1989), pp. 123–127 [in Russian].

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  27. K. I. Babenko and V. Yu. Petrovich, “On the Rayleigh-Taylor instability,” Preprint No. 68 (Keldysh Institute of Applied Mathematics, Moscow, 1978).

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  28. K. I. Babenko and V. Yu. Petrovich, “On the Rayleigh-Taylor instability,” Sov. Phys. Dokl. 24, 161–163 (1979).

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  29. K. I. Babenko and V. Yu. Petrovich, “Numerical study of the Rayleigh-Taylor instability problem,” Sov. Phys. Dokl. 25, 909–912 (1980).

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  30. K. I. Babenko and V. Yu. Petrovich, “On the Rayleigh-Taylor instability,” in To the 75th Anniversary of Academician A. N. Tikhonov. Topical Problems of Mathematical Physics and Computational Mathematics (Nauka, Moscow, 1984) [in Russian].

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  31. K. I. Babenko, “Computational experiment and demonstrative calculations in the surface wave problem,” Preprint No. 116 (Keldysh Institute of Applied Mathematics, Moscow, 1986).

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  32. K. I. Babenko, “Some remarks on the theory of surface waves of finite amplitude,” Sov. Math. Dokl. 35, 599–603 (1987).

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  33. K. I. Babenko, “A local existence theorem in the theory of surface waves of finite amplitude,” Sov. Math. Dokl. 35, 647–650 (1987).

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  34. K. I. Babenko, V. Yu. Petrovich, and A. I. Rakhmanov, “A computational experiment in the theory of surface waves of finite amplitude,” Sov. Math. Dokl. 38, 327–331 (1988).

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia

    A. I. Aptekarev & N. G. Afendikova

Authors
  1. A. I. Aptekarev
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  2. N. G. Afendikova
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Correspondence to A. I. Aptekarev or N. G. Afendikova.

Additional information

To the memory of K. I. Babenko (on the 100th anniversary of his birth)

Konstantin Ivanovich Babenko (July 21, 1919–June 10, 1987), an outstanding scientist in the field of fluid mechanics, numerical analysis, harmonic analysis, theory of functions, approximation theory, and theory of partial differential equations, Corresponding Member of Academy of Sciences of the USSR (1976); Doctor of Physics and Mathematics (1952), Professor (1958), recipient of the State Award of the USSR, member of the editorial board of the Journal of Applied Mathematics and Mechanics (1978–1987).

Translated by N. Semenova

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Aptekarev, A.I., Afendikova, N.G. About the Works of K. I. Babenko in the Field of Mechanics and Applied Mathematics (on the 100th Anniversary of His Birth). Mech. Solids 55, 919–925 (2020). https://doi.org/10.3103/S0025654420070043

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