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Approximation of Two-Dimensional Viscoelastic Flows of General Form

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We consider the initial-boundary value problem for approximations of the system of integro-differential equations generalizing the equations of motion for viscoelastic fluids. We prove the existence and convergence theorems and give some examples of non-Newtonian fluids described by the model under consideration.

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References

  1. O. A. Ladyzhenskaya and G. A. Seregin, “On a method of approximation of initial boundary value problems for the Navier–Stokes equations,” J. Math. Sci., New York 75, No. 6, 2038-2057 (1995).

  2. A. P. Oskolkov, “Time periodic solutions of smooth convergent dissipative eε-approximations of the modified Navier–Stokes equations,” J. Math. Sci., New York 84, No.1, 888–897 (1997).

  3. A. A. Kotsiolis and A. P. Oskolkov, “The initial boundary-value problem with a free surface condition for the 𝜖-approximations of the Navier-Stokes equations and some their regularizations,” J. Math. Sci., New York 80, No.3, 1773–1801 (1996).

  4. N. A. Karazeeva, “Solvability of initial boundary value problems for equations describing motions of linear viscoelastic fluids,” J. Appl. Math. 2005, No. 1, 59–80 (2005).

  5. A. A. Il’yushin and B. E. Pobedrya, Fundamentals of the Mathematical Theory of Thermal Viscoelasticity [in Russian], Nauka, Moscow (1970).

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

  7. M. A. Krasnosel’skij, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskij, and V. Ya. Stetsenko, Approximate Solution of Operator Equations, Wolters-Noordhoff Publ., Groningen (1972).

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Authors and Affiliations

  1. Steklov Mathematical Institute RAS, 27, nab. Fontanka, St. Petersburg, 191023, Russia

    N. A. Karazeeva

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  1. N. A. Karazeeva
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Correspondence to N. A. Karazeeva.

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Dedicated to the memory of Vasilii Vasil’evich Zhikov

Translated from Problemy Matematicheskogo Analiza 92, 2018, pp. 147-157.

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Karazeeva, N.A. Approximation of Two-Dimensional Viscoelastic Flows of General Form. J Math Sci 232, 378–389 (2018). https://doi.org/10.1007/s10958-018-3878-x

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  • DOI: https://doi.org/10.1007/s10958-018-3878-x

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