Abstract
The two-dimensional system of Navier–Stokes equations in a medium with anisotropic variable viscosity and periodic small obstacles is considered. It is proved that the trajectory attractors of the system tend in a certain weak topology to the trajectory attractors of the homogenized system of Navier–Stokes equations with an additional potential in a medium without obstacles.
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ACKNOWLEDGMENTS
The authors are grateful to V.V. Chepyzhov for helpful discussions of this work and advice concerning a better presentation of the results.
The authors also thank the anonymous peer reviewers for carefully reading the manuscript and providing comments that have helped significantly improve it.
Funding
The research presented in Section 2 was supported by the Ministry of Science and Higher Education of the Republic of Kazakhstan, grant AR14869553. The third author’s work presented in Section 3 was supported by the Ministry of Science and Higher Education of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics, agreement no. 075-15-2022-284.
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Translated by I. Ruzanova
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Bekmaganbetov, K.A., Toleubay, A.M. & Chechkin, G.A. On Asymptotics of Attractors of the Navier–Stokes System in Anisotropic Medium with Small Periodic Obstacles. Dokl. Math. 108, 277–281 (2023). https://doi.org/10.1134/S1064562423700813
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DOI: https://doi.org/10.1134/S1064562423700813