On the existence of fibered three-dimensional perfect fluid equilibria without continuous Euclidean symmetry
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| Format: | Preprint |
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2025
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| _version_ | 1866916994453864448 |
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| author | Drivas, Theodore D. Elgindi, Tarek M. Ginsberg, Daniel |
| author_facet | Drivas, Theodore D. Elgindi, Tarek M. Ginsberg, Daniel |
| contents | Following Lortz, we construct a family of smooth steady states of the ideal, incompressible Euler equation in three dimensions that possess no continuous Euclidean symmetry. As in Lortz, they do possess a planar reflection symmetry and, as such, all the orbits of the velocity are closed. Different from Lortz, our construction has a discrete m-fold symmetry and is foliated by invariant cylindrical level sets of a non-degenerate Bernoulli pressure. Such examples narrow the scope of validity of Grad's conjecture that the only solutions with a continuous symmetry can be fibered by pressure surfaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_02955 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the existence of fibered three-dimensional perfect fluid equilibria without continuous Euclidean symmetry Drivas, Theodore D. Elgindi, Tarek M. Ginsberg, Daniel Analysis of PDEs Fluid Dynamics Plasma Physics 35Q31, 76B03, 76W05 Following Lortz, we construct a family of smooth steady states of the ideal, incompressible Euler equation in three dimensions that possess no continuous Euclidean symmetry. As in Lortz, they do possess a planar reflection symmetry and, as such, all the orbits of the velocity are closed. Different from Lortz, our construction has a discrete m-fold symmetry and is foliated by invariant cylindrical level sets of a non-degenerate Bernoulli pressure. Such examples narrow the scope of validity of Grad's conjecture that the only solutions with a continuous symmetry can be fibered by pressure surfaces. |
| title | On the existence of fibered three-dimensional perfect fluid equilibria without continuous Euclidean symmetry |
| topic | Analysis of PDEs Fluid Dynamics Plasma Physics 35Q31, 76B03, 76W05 |
| url | https://arxiv.org/abs/2510.02955 |