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Global Well-Posedness and Convergence Results for the 3D-Regularized Boussinesq System
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- Journal:
- Canadian Journal of Mathematics / Volume 64 / Issue 6 / 01 December 2012
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1415-1435
- Print publication:
- 01 December 2012
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- Article
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Analytical study of the regularization of the Boussinesq system is performed in frequency space using Fourier theory. Existence and uniqueness of weak solutions with minimum regularity requirement are proved. Convergence results of the unique weak solution of the regularized Boussinesq system to a weak Leray–Hopf solution of the Boussinesq system are established as the regularizing parameter
$\alpha$ vanishes. The proofs are done in the frequency space and use energy methods, the Arselà-Ascoli compactness theorem and a Friedrichs-like approximation scheme.
