Global Solutions and Asymptotic Study to a 3D-Lagrangian Boussinesq System
We prove that the Lagrangian-averaged 3D periodic Boussinesq system has a global in time weak solution that depends continuously on time. Also, we establish that a unique strong global in time solution exists. Moreover, we show that the system has a compact global attractor which is connected. The...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2025-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/jom/5583149 |
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| Summary: | We prove that the Lagrangian-averaged 3D periodic Boussinesq system has a global in time weak solution that depends continuously on time. Also, we establish that a unique strong global in time solution exists. Moreover, we show that the system has a compact global attractor which is connected. The proofs are based on the energy methods and the absorbing balls technics. We utilize the coupling between the mean free temperature and the velocity field to close the energy estimates independently on time. This allows us to obtain global in time solutions and a global attractor. |
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| ISSN: | 2314-4785 |