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

Abstract

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).