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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2604.12091 |
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| _version_ | 1866911591451066368 |
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| author | Giardi, Matteo Székelyhidi Jr, László |
| author_facet | Giardi, Matteo Székelyhidi Jr, László |
| contents | For any $0\leq γ< 1/5$, we construct weak solutions $(v, B, p )$ of the Ideal MHD Equations which do not conserve the total kinetic energy, the cross-helicity and lie in $C^γ(\mathbb{T}^3\times\mathbb{R})$. In the spirit of Arnold's formulation of ideal hydrodynamics, a solution is thought of as a path of volume-preserving diffeomorphisms; the proof is then based on the interplay between classical convex integration techniques and geometric constructions at the level of the Lie algebra of this Lie group. Our work substantially extends the recent work of and building on the recent work of Enciso, Peñafiel-Tomás and Peralta-Salas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12091 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $C^{1/5^{-}}$ Convex Integration Solutions of Ideal MHD Giardi, Matteo Székelyhidi Jr, László Analysis of PDEs 35Q35, 76W05 For any $0\leq γ< 1/5$, we construct weak solutions $(v, B, p )$ of the Ideal MHD Equations which do not conserve the total kinetic energy, the cross-helicity and lie in $C^γ(\mathbb{T}^3\times\mathbb{R})$. In the spirit of Arnold's formulation of ideal hydrodynamics, a solution is thought of as a path of volume-preserving diffeomorphisms; the proof is then based on the interplay between classical convex integration techniques and geometric constructions at the level of the Lie algebra of this Lie group. Our work substantially extends the recent work of and building on the recent work of Enciso, Peñafiel-Tomás and Peralta-Salas. |
| title | $C^{1/5^{-}}$ Convex Integration Solutions of Ideal MHD |
| topic | Analysis of PDEs 35Q35, 76W05 |
| url | https://arxiv.org/abs/2604.12091 |