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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2603.21800 |
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| _version_ | 1866915883158339584 |
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| author | Chen, Zipeng Liu, Song Yin, Zhaoyang |
| author_facet | Chen, Zipeng Liu, Song Yin, Zhaoyang |
| contents | Recently, Coiculescu and Palasek \cite{Coiculescu2025} shows the non-uniqueness of solutions for the 3D incompressible Navier-Stokes equations with initial data in $BMO^{-1}$. Inspired by their breakthrough work, we develop their schemes for the incompressible magnetohydrodynamic equations and obtain a similar result in 5 dimensional case. More precisely, we construct two distinct global solutions with a initial data, which has nonvanishing velocity and magnetic fields in $BMO^{-1}(\mathbb{T}^5)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21800 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-uniqueness of smooth solutions of the 5D magnetohydrodynamic equations from critical data Chen, Zipeng Liu, Song Yin, Zhaoyang Analysis of PDEs Recently, Coiculescu and Palasek \cite{Coiculescu2025} shows the non-uniqueness of solutions for the 3D incompressible Navier-Stokes equations with initial data in $BMO^{-1}$. Inspired by their breakthrough work, we develop their schemes for the incompressible magnetohydrodynamic equations and obtain a similar result in 5 dimensional case. More precisely, we construct two distinct global solutions with a initial data, which has nonvanishing velocity and magnetic fields in $BMO^{-1}(\mathbb{T}^5)$. |
| title | Non-uniqueness of smooth solutions of the 5D magnetohydrodynamic equations from critical data |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.21800 |