  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$ ${\rho}^{0}{\in}B_{2,1}^{1/2}(\RR^3)\cap
L^{p}(\RR^3)$ 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.
