Global Well-Posedness and Convergence Results to a 3D Regularized Boussinesq System in Sobolev Spaces

Ridha Selmi, Shahah Almutairi and Yongqiang Fu

Journal of Mathematics, 2024, vol. 2024, 1-6

Abstract: We consider a regularized periodic three-dimensional Boussinesq system. For a mean free initial temperature, we use the coupling between the velocity and temperature to close the energy estimates independently of time. This allows proving the existence of a global in time unique weak solution. Also, we establish that this solution depends continuously on the initial data. Moreover, we prove that this solution converges to a Leray-Hopf weak solution of the three-dimensional Boussinesq system as the regularizing parameter vanishes.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:4495266

DOI: 10.1155/2024/4495266

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