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Well-posedness and convergence results for the 3D-Lagrange Boussinesq-\(\alpha \) system

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Abstract

In this paper, we study the three-dimensional Lagrangian averaged Boussinesq-\(\alpha \) system which is a regularized version of the three-dimensional Boussinesq system. We prove the existence of a weak solution to the 3D-Lagrangian averaged Boussinesq-\(\alpha \) system, in Sobolev spaces. Unlike preceding works, this solution is global in time and depends continuously on the initial data, in particular, it is unique. More importantly, it converges to a weak solution of the three-dimensional Boussinesq system, as the regularizing parameter \(\alpha \) vanishes.

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Acknowledgements

The authors gratefully acknowledge the approval and the support of this research study by the Grant No. 7542-SAT-2017-1-8-F from the Deanship of Scientific Research at Northern Border University, Arar, KSA.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences and Art (TURAIF), Northern Border University, Arar, Kingdom of Saudi Arabia

    Abir Sboui

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

    Ridha Selmi

  3. Department of Mathematics, ISSATM, University of Carthage, Carthage, Tunisia

    Abir Sboui

  4. Department of Mathematics, Faculty of Sciences of Gabes, University of Gabes, Gabes, 6072, Tunisia

    Ridha Selmi

  5. Laboratory of Partial Differential Equations and Applications (LR03ES04), Faculty of Sciences of Tunis, University of Tunis El Manar, Tunis, 1068, Tunisia

    Abir Sboui & Ridha Selmi

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  1. Abir Sboui
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  2. Ridha Selmi
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Correspondence to Ridha Selmi.

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Sboui, A., Selmi, R. Well-posedness and convergence results for the 3D-Lagrange Boussinesq-\(\alpha \) system. Arch. Math. 119, 89–100 (2022). https://doi.org/10.1007/s00013-022-01729-x

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  • DOI: https://doi.org/10.1007/s00013-022-01729-x

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