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

2021/10/27 by Hanachi, Adalet, Houamed, Haroune, Zerguine, Mohamed
#35B33 #35Q30 #35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2110.14208

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 \citeHanachi-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 \citeGallay-Sverak, we prove the global wellposedness result provided that the atomic parts of the initial measures are small enough.

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