Nonlinear instability for the 3D MHD equations around the Taylor-Couette flow
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908592934748160 |
|---|---|
| author | Navarro-Fernández, Víctor Villringer, David |
| author_facet | Navarro-Fernández, Víctor Villringer, David |
| contents | We study the 3D magnetohydrodynamics (MHD) equations in an annular cylinder, perturbed around the explicit steady state given by the 3D Taylor-Couette velocity field and zero magnetic field. Combining a recent linear instability result for the magnetic field with the framework of Friedlander, Pavlović and Shvydkoy [Comm. Math. Phys. 264 (2006), no. 2, 335-347], we prove nonlinear instability of the solution around this steady state in $L^p$, for any $p>1$. In particular, our results are, to the best of our knowledge, the first rigorous instability results for 3D MHD without forcing, in which the instability is produced as a result of the (exponential) growth of the magnetic field. Furthermore, we offer a mathematical proof of the physically conjectured transfer of energy from the velocity field to the magnetic field in the MHD system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12707 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear instability for the 3D MHD equations around the Taylor-Couette flow Navarro-Fernández, Víctor Villringer, David Analysis of PDEs We study the 3D magnetohydrodynamics (MHD) equations in an annular cylinder, perturbed around the explicit steady state given by the 3D Taylor-Couette velocity field and zero magnetic field. Combining a recent linear instability result for the magnetic field with the framework of Friedlander, Pavlović and Shvydkoy [Comm. Math. Phys. 264 (2006), no. 2, 335-347], we prove nonlinear instability of the solution around this steady state in $L^p$, for any $p>1$. In particular, our results are, to the best of our knowledge, the first rigorous instability results for 3D MHD without forcing, in which the instability is produced as a result of the (exponential) growth of the magnetic field. Furthermore, we offer a mathematical proof of the physically conjectured transfer of energy from the velocity field to the magnetic field in the MHD system. |
| title | Nonlinear instability for the 3D MHD equations around the Taylor-Couette flow |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.12707 |