Global strong solutions of the tropical climate model with temperature-dependent diffusion on the barotropic mode

This paper is concerned with the tropical model with temperature-dependent diffusion on the barotropic mode in R2×R+. We prove the existence of the global strong solution under the initial data ‖u0‖Hs2+‖v0‖Hs2+‖θ0‖Hs2 with s>1 is suitably small.