Global strong solutions of the 2D tropical climate system with temperature-dependent viscosity

Abstract

In this paper, we consider the tropical climate model with temperature-dependent viscosity in $${\mathbb {R}}^{2}$$. We obtain the global strong solution provided that the initial data $$\Vert v_{0}\Vert _{H^{s}}^{2}+\Vert \theta _{0}\Vert _{H^{s}}^{2}(s>1)$$ are small enough. It is worth to point out that there is no any smallness condition on the barotropic mode u.