Two improved Liouville-type theorems for the 3D stationary tropical climate model without temperature assumptions
Abstract
In this paper, we establish two improved Liouville-type theorems for the three-dimensional stationary tropical climate model without imposing any temperature assumptions. Compared with previous results, we achieve significant improvements on the growth assumptions imposed on u, v and ∇ v. Owing to the special structure inherent to the equations, we fully exploit the L2-estimate for the oscillation of the temperature, refined interpolation techniques and an iteration argument to establish a Liouville-type theorem under flexible and relaxed power-law growth conditions. As an interesting consequence, we obtain the triviality of solutions under the integrability conditions imposed only on (u,∇ v) or (∇ u,∇ v). Furthermore, by developing a systematic framework to handle the energy function associated with the non-trivial solutions and with the aid of delicate ODE analysis and a contradiction argument, we refine our Liouville-type theorem by introducing logarithmic corrections to the growth rates.
Related
- Liouville Theorems for the Stationary Fractional Hall-Magnetohydrodynamic Equations
- Liouville theorems for the stationary Navier-Stokes equations under partial component conditions
- Liouville Theorems for the Stationary Fractional Magnetohydrodynamic Equations
- Liouville Theorems for Stationary Navier-Stokes Equations via the Radial Velocity Component
- Liouville-type theorems and perturbation uniqueness for stationary incompressible MHD with directional fractional dissipation
BibTeX
@misc{zhang2026improved,
title = {{Two improved Liouville-type theorems for the 3D stationary tropical climate model without temperature assumptions}},
author = {Zhibing Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.13149},
eprint = {2608.13149},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.13149},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Two improved Liouville-type theorems for the 3D stationary tropical climate model without temperature assumptions
AU - Zhibing Zhang
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2608.13149
UR - https://arxiv.org/abs/2608.13149
AB - In this paper, we establish two improved Liouville-type theorems for the three-dimensional stationary tropical climate model without imposing any temperature assumptions. Compared with previous results, we achieve significant improvements on the growth assumptions imposed on u, v and ∇ v. Owing to the special structure inherent to the equations, we fully exploit the L^2-estimate for the oscillation of the temperature, refined interpolation techniques and an iteration argument to establish a Liouville-type theorem under flexible and relaxed power-law growth conditions. As an interesting consequence, we obtain the triviality of solutions under the integrability conditions imposed only on (u,∇ v) or (∇ u,∇ v). Furthermore, by developing a systematic framework to handle the energy function associated with the non-trivial solutions and with the aid of delicate ODE analysis and a contradiction argument, we refine our Liouville-type theorem by introducing logarithmic corrections to the growth rates.
ER -