The primitive equations for the ocean and atmosphere in anisotropic spaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909682526846976 |
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| author | Lemarié, Valentin |
| author_facet | Lemarié, Valentin |
| contents | In this work, we study the well-posedness of the primitive equations for the ocean and the atmosphere on two specific domains: a bounded domain $Ω_1\mathrel{\mathop:}=(-1,1)^3$ with periodic boundary conditions, and the strip $Ω_2\mathrel{\mathop:}=\mathbb{R}^2\times(-1,1)$ with periodic boundary conditions in the vertical direction. In a first time, we establish a global existence and uniqueness theorem for small initial data in a suitable anisotropic Besov space. Then, we also justify, in a similar functional framework, the singular limit from the anisotropic Navier-Stokes equations to this system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07546 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The primitive equations for the ocean and atmosphere in anisotropic spaces Lemarié, Valentin Analysis of PDEs In this work, we study the well-posedness of the primitive equations for the ocean and the atmosphere on two specific domains: a bounded domain $Ω_1\mathrel{\mathop:}=(-1,1)^3$ with periodic boundary conditions, and the strip $Ω_2\mathrel{\mathop:}=\mathbb{R}^2\times(-1,1)$ with periodic boundary conditions in the vertical direction. In a first time, we establish a global existence and uniqueness theorem for small initial data in a suitable anisotropic Besov space. Then, we also justify, in a similar functional framework, the singular limit from the anisotropic Navier-Stokes equations to this system. |
| title | The primitive equations for the ocean and atmosphere in anisotropic spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.07546 |