Large global solutions to 3D Boussinesq equations slowly varying in one direction

In this paper, we investigate the global well-posedness for the 3D Boussinesq equations. Firstly, we prove the global existence and uniqueness of the solution in critical space for small initial data. Then, aimed at the large initial data giving rise to global solution, we obtain a certain class of large solutions with initial data slowly varying in one direction. The proof relies on the special structure of the equation and some new refined estimates for the velocity and temperature.