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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2406.01104 |
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| _version_ | 1866916271187034112 |
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| author | Lemarié, Valentin |
| author_facet | Lemarié, Valentin |
| contents | We study the well-posedness of the primitive equations for the ocean and atmosphere on two particular domains : a bounded domain $Ω_1 := (-1, 1)^3$ with periodic boundary conditions and the strip $Ω_2 := \mathbb{R}^2 \times (-1, 1)$ with a periodic boundary condition for the vertical coordinate. An existence theorem for global solutions on a suitable Besov space is derived. Then, in a second step, we rigorously justify the passage to the limit from the rescaled anisotropic Navier-Stokes equations to these primitive equations in the same functional framework as that found for the solutions of the primitive equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01104 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From anisotropic Navier-Stokes equations to primitive equations for the ocean and atmosphere Lemarié, Valentin Analysis of PDEs We study the well-posedness of the primitive equations for the ocean and atmosphere on two particular domains : a bounded domain $Ω_1 := (-1, 1)^3$ with periodic boundary conditions and the strip $Ω_2 := \mathbb{R}^2 \times (-1, 1)$ with a periodic boundary condition for the vertical coordinate. An existence theorem for global solutions on a suitable Besov space is derived. Then, in a second step, we rigorously justify the passage to the limit from the rescaled anisotropic Navier-Stokes equations to these primitive equations in the same functional framework as that found for the solutions of the primitive equations. |
| title | From anisotropic Navier-Stokes equations to primitive equations for the ocean and atmosphere |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.01104 |