Email this article 
ON ASYMPTOTICS OF ATTRACTORS TO NAVIER-STOCKES SYSTEM IN ANISOTROPIC MEDIUM WITH SMALL PERIODIC OBSTACLES
- Authors: Bekmaganbetov К.А.1,2, Toleubay А.М.3,2, Chechkin G.А.4,5,2
-
Affiliations:
- Lomonosov Moscow State University, Kazakhstan Branch
- Institute of Mathematics and Mathematical Modeling
- Eurasian National University named after L.N. Gumilyov
- 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
- Issue: Vol 512, No 1 (2023)
- Pages: 42-46
- Section: MATHEMATICS
- URL: https://journal-vniispk.ru/2686-9543/article/view/139273
- DOI: https://doi.org/10.31857/S2686954322600549
- EDN: https://elibrary.ru/PJZJPW
- ID: 139273
Cite item
Open Access
Access granted
Subscription 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 Centerof 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
- 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.
- Chepyzhov V.V., Vishik M.I. Evolution equations and their trajectory attractors // J. Math. Pures Appl. 1997. V. 76. № 10. P. 913–964.
- 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.
- 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.
- 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.
- 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.
- 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.
- Бабин А.В., Вишик М.И. Аттракторы эволюционных уравнений. М.: Наука, 1989.
- Chepyzhov V.V., Vishik M.I. Attractors for equations of mathematical physics. Providence (RI): Amer. Math. Soc., 2002.
- Temam R. Navier–Stokes equations: Theory and numerical analysis. Amsterdam–New York–Oxford: North Holland, 1979.
- Temam R. Infinite-dimensional dynamical systems in mechanics and physics. Applied Mathematics Series. V. 68. New York (NY): Springer-Verlag, 1988.
- 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.
- 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.
- 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.
- 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
