An improved Liouville-type theorem for the stationary tropical climate model

Abstract

In this paper, we study the Liouville-type property for smooth solutions to the steady 3D tropical climate model. We prove that if a smooth solution $(u,v,\theta)$ satisfies $u \in L^3 (\mathbb{R}^3)$, $v \in L^2 (\mathbb{R}^3)$, and $\nabla \theta \in L^2 (\mathbb{R}^3)$, then $u=v=0$ and $\theta$ is constant, which improves the previous result, Theorem 1.3 (Math. Methods Appl. Sci. 44, 2021) by Ding and Wu.