Nonlinear stability and long-time dynamics of 3D Boussinesq-Coriolis equations in critical spaces

In this paper, we investigate the nonlinear dynamics of a three-dimensional rescaled Boussinesq system with Coriolis force, positive diffusivity, and viscosity, arising in rotating stratified fluid models. By introducing a suitable rescaling of the velocity and temperature fields, we analyze the resulting system in critical Fourier-Besov-Morrey spaces that allow homogeneous functions of negative degree. Sharp estimates for the associated linear semigroup and the bilinear nonlinear interactions are established, leading to a robust control of the nonlinear dynamics. As a consequence, we prove the existence and uniqueness of global mild solutions for small initial data by means of a fixed-point argument in an appropriate functional setting.