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arXiv · 2110.14208

Remarks on the global well-posedness of the axisymmetric Boussinesq system with rough initial data

Adalet Hanachi·Haroune Houamed·Mohamed Zerguine
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Abstract

This work concerns the global well-posedness problem for the 3D axisymmetric viscous Boussinesq system with critical rough initial data. More precisely, we aim to extending our recent result \cite{Hanachi-Houamed-Zerguine} to the case of initial data of measure type. To this end, we should first develop some notions of axisymmetric measures in a general context, then, in the spirit of \cite{Gallay-Sverak}, we prove the global wellposedness result provided that the atomic parts of the initial measures are small enough.

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Adalet Hanachi, Haroune Houamed, Mohamed Zerguine. 2021-10-27. Remarks on the global well-posedness of the axisymmetric Boussinesq system with rough initial data. https://arxiv.org/abs/2110.14208

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