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

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,...

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Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2024, Vol.2024, p.1-6
Main Authors: Selmi, Ridha, Almutairi, Shahah
Format: Article
Language:English
Subjects:
Boussinesq equations
Convergence
Fourier transforms
Inequality
Navier-Stokes equations
Partial differential equations
Physicists
Sobolev space
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Summary: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.
ISSN:2314-4629
2314-4785
DOI:10.1155/2024/4495266