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 a 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.