Trajectory and Global Attractors for the Kelvin–Voigt Model Taking into Account Memory along Fluid Trajectories
This article is devoted to the study of the existence of trajectory and global attractors in the Kelvin–Voigt fluid model, taking into account memory along the trajectories of fluid motion. For the model under study, the concept of a weak solution on a finite segment and semi-axis is introduced and...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/2/266 |
| _version_ | 1797343048462499840 |
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| author | Mikhail Turbin Anastasiia Ustiuzhaninova |
| author_facet | Mikhail Turbin Anastasiia Ustiuzhaninova |
| author_sort | Mikhail Turbin |
| collection | DOAJ |
| description | This article is devoted to the study of the existence of trajectory and global attractors in the Kelvin–Voigt fluid model, taking into account memory along the trajectories of fluid motion. For the model under study, the concept of a weak solution on a finite segment and semi-axis is introduced and the existence of their solutions is proved. The necessary exponential estimates for the solutions are established. Then, based on these estimates, the existence of trajectory and global attractors in the problem under study is proved. |
| first_indexed | 2024-03-08T10:42:03Z |
| format | Article |
| id | doaj.art-2626a6a70e974121bb4d9d955666fd13 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T10:42:03Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2626a6a70e974121bb4d9d955666fd132024-01-26T17:32:33ZengMDPI AGMathematics2227-73902024-01-0112226610.3390/math12020266Trajectory and Global Attractors for the Kelvin–Voigt Model Taking into Account Memory along Fluid TrajectoriesMikhail Turbin0Anastasiia Ustiuzhaninova1Research Institute of Mathematics, Voronezh State University, Universitetskaya pl. 1, 394018 Voronezh, RussiaResearch Institute of Mathematics, Voronezh State University, Universitetskaya pl. 1, 394018 Voronezh, RussiaThis article is devoted to the study of the existence of trajectory and global attractors in the Kelvin–Voigt fluid model, taking into account memory along the trajectories of fluid motion. For the model under study, the concept of a weak solution on a finite segment and semi-axis is introduced and the existence of their solutions is proved. The necessary exponential estimates for the solutions are established. Then, based on these estimates, the existence of trajectory and global attractors in the problem under study is proved.https://www.mdpi.com/2227-7390/12/2/266trajectory attractorglobal attractorKelvin–Voigt modelregular Lagrangian flowboundary value problemnon-Newtonian fluid |
| spellingShingle | Mikhail Turbin Anastasiia Ustiuzhaninova Trajectory and Global Attractors for the Kelvin–Voigt Model Taking into Account Memory along Fluid Trajectories Mathematics trajectory attractor global attractor Kelvin–Voigt model regular Lagrangian flow boundary value problem non-Newtonian fluid |
| title | Trajectory and Global Attractors for the Kelvin–Voigt Model Taking into Account Memory along Fluid Trajectories |
| title_full | Trajectory and Global Attractors for the Kelvin–Voigt Model Taking into Account Memory along Fluid Trajectories |
| title_fullStr | Trajectory and Global Attractors for the Kelvin–Voigt Model Taking into Account Memory along Fluid Trajectories |
| title_full_unstemmed | Trajectory and Global Attractors for the Kelvin–Voigt Model Taking into Account Memory along Fluid Trajectories |
| title_short | Trajectory and Global Attractors for the Kelvin–Voigt Model Taking into Account Memory along Fluid Trajectories |
| title_sort | trajectory and global attractors for the kelvin voigt model taking into account memory along fluid trajectories |
| topic | trajectory attractor global attractor Kelvin–Voigt model regular Lagrangian flow boundary value problem non-Newtonian fluid |
| url | https://www.mdpi.com/2227-7390/12/2/266 |
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