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

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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

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