Zeitlin's model for axisymmetric 3-D Euler equations
<|reference_start|>Zeitlin's model for axisymmetric 3-D Euler equations: 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. Thus, this finite-dimensional model admits Riemannian curvature and Jacobi equations, which are discussed.<|reference_end|>
@article{modin2024zeitlin's,
    title={Zeitlin's model for axisymmetric 3-D Euler equations},
    author={Klas Modin and Stephen C. Preston},
    journal={arXiv preprint arXiv:2408.11204},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.11204},
    primaryClass={math.DG cs.NA math-ph math.MP math.NA}
}