ON ASYMPTOTICS OF ATTRACTORS TO NAVIER-STOCKES SYSTEM IN ANISOTROPIC MEDIUM WITH SMALL PERIODIC OBSTACLES

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

The paper considers a two-dimensional system of Navier–Stokes equations in medium with anisotropic variable viscosity and periodic small obstacles. It is proved that the trajectory attractors of this system tend in a certain weak topology to the trajectory attractors of the averaged system of Navier–Stokes equations with an additional potential in a medium without obstacles.

About the authors

К. А. Bekmaganbetov

Lomonosov Moscow State University, Kazakhstan Branch; Institute of Mathematics and Mathematical Modeling

Author for correspondence.
Email: bekmaganbetov-ka@yandex.kz
Kazakhstan, Astana; Kazakhstan, Almaty

А. М. Toleubay

Eurasian National University named after L.N. Gumilyov; Institute of Mathematics and Mathematical Modeling

Author for correspondence.
Email: altyn.15.94@mail.ru
Kazakhstan, Astana; Kazakhstan, Almaty

G. А. Chechkin

Moscow State University. M.V. Lomonosov; Institute of Mathematics with a Computer Center – a division of the Ufa Federal Research Center
of the Russian Academy of Sciences; Institute of Mathematics and Mathematical Modeling

Author for correspondence.
Email: chechkin@mech.math.msu.su
Russian Federation, Moscow; Russian Federation, Ufa; Kazakhstan, Almaty

References

  1. Chepyzhov V.V., Vishik M.I. Non-autonomous 2D Navier–Stokes system with singularly oscillating external force and its global attractor // J. Dyn. Diff. Eqns. 2007. V. 19. P. 655–684.
  2. Chepyzhov V.V., Vishik M.I. Evolution equations and their trajectory attractors // J. Math. Pures Appl. 1997. V. 76. № 10. P. 913–964.
  3. Самохин В.Н., Фадеева Г.М., Чечкин Г.А. Уравнения пограничного слоя для модифицированной системы Навье–Стокса // Труды семинара им. И.Г. Петровского. Вып. 28. М.: Изд-во Моск. ун-та, 2011. С. 329–361.
  4. Chechkin G.A., Chechkina T.P., Ratiu T.S., Romanov M.S. Nematodynamics and Random Homogenization // Applicable Analysis. 2016. V. 95. № 10. P. 2243–2253.
  5. Бекмаганбетов К.А., Чечкин Г.А., Чепыжов В.В. Сильная сходимость аттракторов системы реакции–диффузии с быстро осциллирующими членами в ортотропной пористой среде // Известия РАН. 2022. Т. 86. № 6. С. 3–34.
  6. Bekmaganbetov K.A., Chechkin G.A., Chepyzhov V.V. “Strange Term” in Homogenization of Attractors of Reaction–Diffusion Equation in Perforated Domain // Chaos, Solitons & Fractals. 2020. V. 140. Art. No 110208.
  7. Бекмаганбетов К.А., Толеубай А.М., Чечкин Г.А. Об аттракторах системы уравнений Навье–Стокса в двумерной пористой среде // Проблемы математического анализа. 2022. Т. 115. С. 15–28.
  8. Бабин А.В., Вишик М.И. Аттракторы эволюционных уравнений. М.: Наука, 1989.
  9. Chepyzhov V.V., Vishik M.I. Attractors for equations of mathematical physics. Providence (RI): Amer. Math. Soc., 2002.
  10. Temam R. Navier–Stokes equations: Theory and numerical analysis. Amsterdam–New York–Oxford: North Holland, 1979.
  11. Temam R. Infinite-dimensional dynamical systems in mechanics and physics. Applied Mathematics Series. V. 68. New York (NY): Springer-Verlag, 1988.
  12. Conca C. Mathematical modeling of the steam-water condensation in a condenser. Large-scale computations in fluid mechanics, Part 1 (La Jolla, Calif., 1983), 87–98, Lectures in Appl. Math., 22-1, Amer. Math. Soc., Providence, RI, 1985.
  13. Conca C. Numerical results on the homogenization of Stokes and Navier-Stokes equations modeling a class of problems from fluid mechanics // Comput. Methods Appl. Mech. Engrg. 1985. V. 53. № 3. P. 223–258.
  14. Conca C. On the application of the homogenization theory to a class of problems arising in fluid mechanics. // J. Math. Pures Appl. 1985. V. 64 (9). № 1. P. 31–75.
  15. Беляев А.Г., Пятницкий А.Л., Чечкин Г.А. Усреднение в перфорированной области с осциллирующим третьим краевым условием // Математический сборник. 2001. Т. 192. № 7. С. 3–20.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2.

Download (519KB)
Indexing metadata

Copyright (c) 2023 К.А. Бекмаганбетов, А.М. Толеубай, Г.А. Чечкин