Global Well-Posedness for the 3D Tropical Climate Model Without Thermal Diffusion

Abstract

In this paper, we consider the Cauchy problem of 3D tropical climate model with zero thermal diffusion. Firstly, we establish the global regularity for this system with fractional diffusion $\alpha=\beta=5/4.$ Secondly, by adding only a damp term, we obtain the global well-posedness for small initial data.