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May 29, 2026ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik0 citations

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

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YCYouseung ChoMYMinsuk Yang

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.

Abstract

ABSTRACT 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.

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Cite This Study

Cho et al. (2026) studied this question.

synapsesocial.com/papers/6a192d4afab5b468c441622bhttps://doi.org/10.1002/zamm.70481
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