A regularity criterion for a 3D tropical climate model with damping

In this paper we deal with the 3D tropical climate model with damping terms in the equation of the barotropic mode $u$ and in the equation of the first baroclinic mode $v$ of the velocity, and we establish a regularity criterion for this system thanks to which the local smooth solution $(u, v, \theta)$ can actually be extended globally in time.Comment: 16 pages. The proof of Theorem 2.1 has been improved by making the higher-order inequalities sharper. Unnecessary estimates have been removed. Minor typos have been fixe