An improved Liouville-type theorem for the stationary tropical climate model
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910283476238336 |
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| author | Cho, Youseung In, Hyunjin Yang, Minsuk |
| author_facet | Cho, Youseung In, Hyunjin Yang, Minsuk |
| contents | In this paper, we study the Liouville-type property for smooth solutions to the steady 3D tropical climate model. We prove that if a smooth solution $(u,v,θ)$ satisfies $u \in L^3 (\mathbb{R}^3)$, $v \in L^2 (\mathbb{R}^3)$, and $\nabla θ\in L^2 (\mathbb{R}^3)$, then $u=v=0$ and $θ$ is constant, which improves the previous result, Theorem 1.3 (Math. Methods Appl. Sci. 44, 2021) by Ding and Wu. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17441 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An improved Liouville-type theorem for the stationary tropical climate model Cho, Youseung In, Hyunjin Yang, Minsuk Analysis of PDEs 35Q35, 35B65, 35A02 In this paper, we study the Liouville-type property for smooth solutions to the steady 3D tropical climate model. We prove that if a smooth solution $(u,v,θ)$ satisfies $u \in L^3 (\mathbb{R}^3)$, $v \in L^2 (\mathbb{R}^3)$, and $\nabla θ\in L^2 (\mathbb{R}^3)$, then $u=v=0$ and $θ$ is constant, which improves the previous result, Theorem 1.3 (Math. Methods Appl. Sci. 44, 2021) by Ding and Wu. |
| title | An improved Liouville-type theorem for the stationary tropical climate model |
| topic | Analysis of PDEs 35Q35, 35B65, 35A02 |
| url | https://arxiv.org/abs/2312.17441 |