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

Abstract

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 $\hat{I}\pm \ge \frac{3}{2}$ and ${\hat{I}}^2\ge 4$. 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 $\hat{I}\pm \ge \frac{3}{2}$ and $4\le {\hat{I}}^2\le 5$.