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New Liouville-type theorem for the stationary tropical climate model

Youseung Cho, Hyunjin In, Minsuk Yang

Abstract

We study the Liouville-type theorem for smooth solutions to the steady 3D tropical climate model. We prove the Liouville-type theorem if a smooth solution satisfies a certain growth condition in terms of $L^p$-norm on annuli, which improves the previous results, Theorem 1.1 (Math. Methods Appl. Sci. 44, 2021) by Ding and Wu, and Theorem 1.1 and Theorem 1.2 (Appl. Math. Lett. 138, 2023) by Yuan and Wang.

New Liouville-type theorem for the stationary tropical climate model

Abstract

We study the Liouville-type theorem for smooth solutions to the steady 3D tropical climate model. We prove the Liouville-type theorem if a smooth solution satisfies a certain growth condition in terms of -norm on annuli, which improves the previous results, Theorem 1.1 (Math. Methods Appl. Sci. 44, 2021) by Ding and Wu, and Theorem 1.1 and Theorem 1.2 (Appl. Math. Lett. 138, 2023) by Yuan and Wang.
Paper Structure (3 sections, 3 theorems, 30 equations)

This paper contains 3 sections, 3 theorems, 30 equations.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Proof of Theorem \ref{['T1']}

Key Result

Theorem 1

Let $(u,v,\theta)$ be a smooth solution to E11. Then $u = v = \theta = 0$ if one of the following conditions holds.

Theorems & Definitions (6)

  • Theorem 1
  • Remark 1
  • Lemma 2: Theorem 3.15 of MR1962933
  • Remark 2
  • Lemma 3
  • proof