On the Global Existence for the Axisymmetric Euler-Boussinesq System in Critical Besov Spaces

This paper is devoted to the global existence and uniqueness results for the three-dimensional Boussinesq system with axisymmetric initial data $v^{0}{\in}B_{2,1}^{5/2}(\RR^3)$ and$$ρ^{0}{\in}B_{2,1}^{1/2}(\RR^3)\cap L^{p}(\RR^3)$with$p>6.$ This system couples the incompressible Euler equations with a transport-diffusion equation governing the density. In this case the Beale-Kato-Majda criterion is not known to be valid and to circumvent this difficulty we use in a crucial way some geometric properties of the vorticity.

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