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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2408.11204 |
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| _version_ | 1866916888733286400 |
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| author | Modin, Klas Preston, Stephen C. |
| author_facet | Modin, Klas Preston, Stephen C. |
| contents | Zeitlin's model is a spatial discretization for the 2-D Euler equations on the flat 2-torus or the 2-sphere. Contrary to other discretizations, it preserves the underlying geometric structure, namely that the Euler equations describe Riemannian geodesics on a Lie group. Here we show how to extend Zeitlin's approach to the axisymmetric Euler equations on the 3-sphere. It is the first discretization of the 3-D Euler equations that fully preserves the geometric structure, albeit restricted to axisymmetric solutions. Thus, this finite-dimensional model admits Riemannian curvature and Jacobi equations, which are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11204 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zeitlin's model for axisymmetric 3-D Euler equations Modin, Klas Preston, Stephen C. Differential Geometry Numerical Analysis Mathematical Physics 35Q31, 53D50, 76M60, 76B47, 53D25 Zeitlin's model is a spatial discretization for the 2-D Euler equations on the flat 2-torus or the 2-sphere. Contrary to other discretizations, it preserves the underlying geometric structure, namely that the Euler equations describe Riemannian geodesics on a Lie group. Here we show how to extend Zeitlin's approach to the axisymmetric Euler equations on the 3-sphere. It is the first discretization of the 3-D Euler equations that fully preserves the geometric structure, albeit restricted to axisymmetric solutions. Thus, this finite-dimensional model admits Riemannian curvature and Jacobi equations, which are discussed. |
| title | Zeitlin's model for axisymmetric 3-D Euler equations |
| topic | Differential Geometry Numerical Analysis Mathematical Physics 35Q31, 53D50, 76M60, 76B47, 53D25 |
| url | https://arxiv.org/abs/2408.11204 |