Analysis of a three-dimensional rapidly rotating convection model without thermal diffusion
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916855660150784 |
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| author | Cao, Chongsheng Guo, Yanqiu Titi, Edriss S. |
| author_facet | Cao, Chongsheng Guo, Yanqiu Titi, Edriss S. |
| contents | We study a three-dimensional rapidly rotating convection model featuring tall columnar structures, in the absence of thermal diffusion. We establish the global existence and uniqueness of weak solutions, as well as the Hadamard well-posedness of global strong solutions to this model. The lack of thermal diffusion introduces significant challenges in the analysis. To overcome these challenges, we first investigate the regularized model with thermal diffusion and establish delicate estimates that are independent of the thermal diffusion coefficient, and consequently justify the vanishing diffusivity limit. This work serves as a continuation of our previous paper [6]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16143 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis of a three-dimensional rapidly rotating convection model without thermal diffusion Cao, Chongsheng Guo, Yanqiu Titi, Edriss S. Analysis of PDEs 35Q35, 35A01, 35A02 We study a three-dimensional rapidly rotating convection model featuring tall columnar structures, in the absence of thermal diffusion. We establish the global existence and uniqueness of weak solutions, as well as the Hadamard well-posedness of global strong solutions to this model. The lack of thermal diffusion introduces significant challenges in the analysis. To overcome these challenges, we first investigate the regularized model with thermal diffusion and establish delicate estimates that are independent of the thermal diffusion coefficient, and consequently justify the vanishing diffusivity limit. This work serves as a continuation of our previous paper [6]. |
| title | Analysis of a three-dimensional rapidly rotating convection model without thermal diffusion |
| topic | Analysis of PDEs 35Q35, 35A01, 35A02 |
| url | https://arxiv.org/abs/2507.16143 |