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Mathematical study of attractors to a 3D heated fluid

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Abstract

The Bardina model to regularize the three-dimensional periodic Boussinesq system is shown to have a global uniform attractor. A mean free initial temperature enables estimates that are from the first step time independent. This allows one to avoid classical technical difficulties generated by the buoyancy force while deriving absorbing balls for which all final bounds depend only on the viscosity, the thermal diffusivity, the regularizing parameter, and the heating source. Also, these bounds are valid for all positive times, not only for large times as it was usually the case due to the buoyancy force in precedent works related to the Boussinesq system.

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Acknowledgements

The authors gratefully acknowledge the approval and the support of this research study by the grant no. SCIA-2022-11-1518 from the Deanship of Scientific Research at Northern Border University, Arar, K.S.A.

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Authors and Affiliations

  1. Department of Mathematics College of Science, Northern Border University, P.O. Box 1321, Arar, 73222, Kingdom of Saudi Arabia

    H. Louati, A. Touati, R. Selmi, A. Aljohani & M. M. Alruwaili

  2. Laboratory of PDEs and Applications (LR03ES04) Faculty of Science of Tunis, University of Tunis El Manar, Tunis, 1068, Tunisia

    H. Louati, A. Touati & R. Selmi

  3. Department of Mathematics, Faculty of Science of Gabès, University of Gabès, Gabès, 6000, Tunisia

    R. Selmi

  4. Laboratory of Dynamical Systems (LR13ES20), Faculty of Science of Sfax University of Sfax, Sfax, 3000, Tunisia

    A. Touati

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  1. H. Louati
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Correspondence to R. Selmi.

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Louati, H., Touati, A., Selmi, R. et al. Mathematical study of attractors to a 3D heated fluid. Arch. Math. 121, 317–328 (2023). https://doi.org/10.1007/s00013-023-01888-5

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  • DOI: https://doi.org/10.1007/s00013-023-01888-5

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