Geodesic interpretation of the global quasi-geostrophic equations
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909579098456064 |
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| author | Modin, Klas Suri, Ali |
| author_facet | Modin, Klas Suri, Ali |
| contents | We give an interpretation of the global shallow water quasi-geostrophic equations on the sphere $\Sph^2$ as a geodesic equation on the central extension of the quantomorphism group on $\Sph^3$. The study includes deriving the model as a geodesic equation for a weak Riemannian metric, demonstrating smooth dependence on the initial data, and establishing global-in-time existence and uniqueness of solutions. We also prove that the Lamb parameter in the model has a stabilizing effect on the dynamics: if it is large enough, the sectional curvature along the trade-wind current is positive, implying conjugate points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10226 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geodesic interpretation of the global quasi-geostrophic equations Modin, Klas Suri, Ali Differential Geometry 58D05, 35Q35, 53C22, 53C80 We give an interpretation of the global shallow water quasi-geostrophic equations on the sphere $\Sph^2$ as a geodesic equation on the central extension of the quantomorphism group on $\Sph^3$. The study includes deriving the model as a geodesic equation for a weak Riemannian metric, demonstrating smooth dependence on the initial data, and establishing global-in-time existence and uniqueness of solutions. We also prove that the Lamb parameter in the model has a stabilizing effect on the dynamics: if it is large enough, the sectional curvature along the trade-wind current is positive, implying conjugate points. |
| title | Geodesic interpretation of the global quasi-geostrophic equations |
| topic | Differential Geometry 58D05, 35Q35, 53C22, 53C80 |
| url | https://arxiv.org/abs/2504.10226 |