Some Liouville Theorems for the 3D Stationary Tropical Climate Model in Lorentz Spaces

ABSTRACT In this paper, we investigate Liouville theorems for the 3D stationary tropical climate model. We obtain that if a smooth solution satisfies some suitable conditions in the setting of Lorentz spaces, there is only trivial solution to the stationary tropical climate model. Moreover, based on the relationship between the stationary tropical climate model and the stationary magnetohydrodynamic (MHD) equations, we obtain Liouville theorems about the MHD equations. Our results extend and generalize some recent results.