The aim of the talk is to provide a rigorous description of the dynamic of non-homogeneous fluids in low Froude number regime. The density profile is considered to be a first-order perturbation of a gravitational equilibrium state. We prove that, in a spatially periodic setting, the evolution equations describing the dynamic of such fluids are globally well-posed in $H^s \left( \mathbb{T}^3\right), s>1/2$.