Remarks on the Anisotropic Liouville Theorem for the Stationary Tropical Climate Model

This paper studies the Liouville type theorems for stationary the tropical climate model on the whole space \(\mathbb{R}^{3}\). It shows that if \((u,v,\theta )\) satisfies certain anisotropic integrability conditions on the components of the \(u\) or \((u,v)\), also \(\theta \) satisfies certain isotropic integrability conditions, there is only a trivial solution to the stationary tropical climate model. The results are a further extension of the recent work by Chae (Appl. Math. Lett. 142:108655, 2023).