Global large solution for the tropical climate model with diffusion

Abstract

We study the $d$-dimensional ($d=2,3$) tropical climate model with only the dissipation of the first baroclinic model of the velocity $-\eta \mathrm{\Delta }v$. By choosing a class of special initial data $\left(u_0,v_0,{𝜃}_0\right)$ whose $H^s\left({ℝ}^d\right)$ norm can be arbitrarily large, we obtain the global smooth solution of $d$-dimensional tropical climate model.