  In this work we prove a global well-posedness result for a tridimensional
rescaled Boussinesq system, with positive full viscosity and diffusivity
parameters in the framework of critical Fourier-Besov spaces. This rescaled
approach permits to know the behaviour of the system according to relations
between both the parameters and the initial velocity and temperature; for
instance, it is possible to consider, for small enough viscosity and large
diffusivity, a large enough critical Fourier-Besov norm for the initial
temperature and it is also possible to consider, for small enough diffusivity
and large viscosity, a large enough critical Fourier-Besov norm for both the
velocity and the temperature.
