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

Key Points

• The study aims to establish Liouville-type theorems for solutions of the stationary tropical climate model without temperature constraints.
• Proved that under certain decay conditions, the only solution is trivial and constant.
• Introduced a key estimate relating oscillation of the velocity components.
• Extended existing theorems with improved energy estimates and new conditions.
• Demonstrated that the trivial solution holds without imposing temperature conditions.
• Verified that the coupling of barotropic and baroclinic velocities leads to constant solutions under mild decay requirements.