Liouville‐Type Theorems for the Stationary Tropical Climate Model Without Temperature Assumptions

We establish Liouville‐type theorems for smooth solutions to the stationary tropical climate model in , which couples barotropic velocity and baroclinic velocity with temperature. Under mild decay conditions on the velocity components, we prove that the only solution is trivial: and is constant. Unlike previous results, our approach imposes no conditions on , thanks to a key estimate linking its oscillation to and . Our results extend and refine existing Liouville‐type theorems via improved energy estimates, annular decay conditions, and an iterative argument.