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Equations of Magnetohydrodynamic Boundary Layer for a Modified Incompressible Viscous Medium. Boundary Layer Separation

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We study the behavior of a magnetohydrodynamic stationary boundary layer of a modified fluid in the sense of Ladyzhenskaya. We study how a magneric force affects the behavior of a continuous medium. We establish the influence of the magnetic field on the point of separation of the boundary layer from the solid streamlined surface.

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References

  1. O. A. Oleinik, “The Prandtl system of equation in boundary layer theory,” Sov. Math., Dokl. 4, 583-586 (1963).

    MATH  Google Scholar 

  2. O. A. Olejnik, “On a system of equations in boundary layer theory,” U.S.S.R. Comput. Math. Math. Phys. 3, 650-673 (1963).

    Article  MathSciNet  MATH  Google Scholar 

  3. O. A. Oleinik, “On the mathematical theory of boundary layer for an unsteady flow of incompressible fluid,” PMM, J. Appl. Math. Mech. 30, No. 5, 951–974 (1966).

    Article  MathSciNet  MATH  Google Scholar 

  4. O. A. Oleinik and V. N. Samokhin, Mathematical Models in Boundary Layer Theory, Chapman & Hall, CRC, Boca Raton, FL (1999).

    MATH  Google Scholar 

  5. Z. P. Shul’man and B. M. Berkovskii, Boundary Layer of Non-Newtonian Fluids [in Russian], Nauka Tekhnika, Minsk (1966).

    Google Scholar 

  6. A. Yu. Linkevich, T. S. Ratiu, S. V. Spiridonov, and G. A. Chechkin, “Thin layer of a non-Newtonian fluid flowing on a rough surface and percolating through a perforated obstacle,” J. Math. Sci., New York 189, No. 3, 525-535 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  7. W. L. Wilkinson, Non-Newtonian Fluids, Pergamon Press, London (1960).

    Google Scholar 

  8. M. Reiner, Lectures on Theoretical Rheology, North-Holland, Amsterdam (1960).

    MATH  Google Scholar 

  9. G. A. Chechkin, T. S. Ratiu, M. S. Romanov, and V. N. Samokhin, “Existence and uniqueness theorems for the two-dimensional Ericksen–Leslie system,” J. Math. Fluid Mech. 18, No. 3, 571–589 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  10. G. A. Chechkin, T. S. Ratiu, M. S. Romanov, and V. N. Samokhin, “On unique solvability of the full three-dimensional Ericksen-Leslie system,” C. R., Méc., Acad. Sci. Paris 344, No. 7, 459–463 (2016).

    Google Scholar 

  11. G. A. Chechkin, T. S. Ratiu, M. S. Romanov, and V. N. Samokhin, “Existence and uniqueness theorems for the full three-dimensional Ericksen–Leslie system,” Math. Models Methods Appl. Sci. 27, No. 5, 807-843 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  12. O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York etc. (1969).

  13. O. A. Ladyzhenskaya, “On modifications of Navier–Stokes equations for large gradients of velocities” [in Russian], Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 7, 126–1543 (1968).

  14. V. N. Samokhin, G. M. Fadeeva, and G. A. Chechkin “Equations of the boundary layer for a modified Navier-Stokes system” J. Math. Sci., New York 179, No. 4, 557-577 (2011).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    P. P. Bulatova & G. A. Chechkin

  2. Moscow Politechnic University, 2A Pryanishnikova St., Moscow, 127550, Russia

    V. N. Samokhin

Authors
  1. P. P. Bulatova
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  2. V. N. Samokhin
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  3. G. A. Chechkin
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Corresponding author

Correspondence to G. A. Chechkin.

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Dedicated to the memory of Vasilii Vasil’evich Zhikov

Translated from Problemy Matematicheskogo Analiza 92, 2018, pp. 83-100.

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Bulatova, P.P., Samokhin, V.N. & Chechkin, G.A. Equations of Magnetohydrodynamic Boundary Layer for a Modified Incompressible Viscous Medium. Boundary Layer Separation. J Math Sci 232, 299–321 (2018). https://doi.org/10.1007/s10958-018-3874-1

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  • DOI: https://doi.org/10.1007/s10958-018-3874-1

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