Abstract
Considering the Bingham fluid motion model, we study the approximation problem, prove its unique solvability, and the existence of attractors. We show that the attractors of the approximation problem converge to the attractors of the Bingham model in the sense of the Hausdorff semidistance in the corresponding metric space as the approximation parameter vanishes.
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Funding
Zvyagin was supported by the Russian Foundation for Basic Research (Grant no. 20–01–00051). Turbin was supported by the Ministry of Science and Higher Education of the Russian Federation (Grant no. FZGU–2020–0035).
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Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 4, pp. 842–859. https://doi.org/10.33048/smzh.2022.63.410
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Zvyagin, V.G., Turbin, M.V. Existence of Attractors for Approximations to the Bingham Model and Their Convergence to the Attractors of the Initial Model. Sib Math J 63, 699–714 (2022). https://doi.org/10.1134/S0037446622040103
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DOI: https://doi.org/10.1134/S0037446622040103
Keywords
- Bingham model
- weak solution
- trajectory attractor
- global attractor
- \( \omega \)-limit set
- Hausdorff semidistance