Global smooth solution for the 3D generalized tropical climate model with partial viscosity and damping

The three-dimensional generalized tropical climate model with partial viscosity and damping is considered in this paper. Global well-posedness of solutions of the three-dimensional generalized tropical climate model with partial viscosity and damping is proved for $\alpha \ge \frac{3}{2}$ and $\beta \ge 4$. Global smooth solution of the three-dimensional generalized tropical climate model with partial viscosity and damping is proved in $H^s({\mathbb{R}}^3)$ $(s>2)$ for $\alpha \ge \frac{3}{2}$ and $4\le \beta \le 5$.