Global strong solutions and large-time behavior of 2D tropical climate model with zero thermal diffusion

In this article, we study the global well-posedness and large-time behaviors of solutions to the two-dimensional tropical climate system with zero thermal diffusion for small initial data in the whole space. The main approaches include high- and low-frequency decomposition method and exploiting the structure of system (1) to obtain the estimates of thermal dissipation. We utilize the time decay properties of the kernels to a linear differential equation to obtain the decay rates of solutions of the low-frequency part and the decay property of exponential operator for the high-frequency part. The key ingredient here is the explicit large-time decay rate of solutions.