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 upsilon(0) is an element of B-2,1(5/2)(R-3) and rho(0) is an element of B-2,1(1/2)(R-3) boolean AND L-p(R-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 (see [2]) is not known to be valid and to circumvent this difficulty we use in a crucial way some geometric properties of the vorticity.