Some remarks on Liouville type theorems for the 3D steady tropical climate model

Observing the special structure of the system and using the Poincar{é}-Sobolev inequality, we establish Liouville type theorems for the 3D steady tropical climate model under certain conditions on $u$, $v$, $\mathrm{\nabla }\theta$. Our results extend and improve a Liouville type result of Cho-In-Yang (arXiv:2312.17441).