Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2508.11193 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911106092498944 |
|---|---|
| author | Peng, Yi Wang, Huaqiao Zhang, Chenlu |
| author_facet | Peng, Yi Wang, Huaqiao Zhang, Chenlu |
| contents | We prove the non-uniqueness of weak solutions with non-trivial magnetic fields to the 3D Hall-MHD equations on the plane in the space $C^0_t L_x^2$ through the convex integration scheme and by constructing new errors and new intermittent flows. In particular, based on the construction of 3D intermittent flows, we obtain the $2\frac{1}{2}$D Mikado flows through a projection onto the plane. Moreover, we prove that the constructed weak solution do not conserve the magnetic helicity and find that weak solutions of the ideal Hall-MHD equations in $C^{\barβ}_{t,x}$ ($\barβ>0$) are the strong vanishing viscosity and resistive limit of weak solutions to the Hall-MHD equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11193 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-uniqueness of weak solutions to the 3D Hall-MHD equations on the plane Peng, Yi Wang, Huaqiao Zhang, Chenlu Analysis of PDEs We prove the non-uniqueness of weak solutions with non-trivial magnetic fields to the 3D Hall-MHD equations on the plane in the space $C^0_t L_x^2$ through the convex integration scheme and by constructing new errors and new intermittent flows. In particular, based on the construction of 3D intermittent flows, we obtain the $2\frac{1}{2}$D Mikado flows through a projection onto the plane. Moreover, we prove that the constructed weak solution do not conserve the magnetic helicity and find that weak solutions of the ideal Hall-MHD equations in $C^{\barβ}_{t,x}$ ($\barβ>0$) are the strong vanishing viscosity and resistive limit of weak solutions to the Hall-MHD equations. |
| title | Non-uniqueness of weak solutions to the 3D Hall-MHD equations on the plane |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.11193 |