Three dimensional stationary solutions of the Electron MHD equations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909675218272256 |
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| author | Peng, Qirui |
| author_facet | Peng, Qirui |
| contents | The goal of this paper is to construct non-trivial steady-state weak solutions of the three dimensional Electron Magnetohydrodynamics equations in the class of $H^s(\mathbb T^3)$ for some small $s > 0$. By exploiting the formulation of the stationary EMHD equations one can treat them as generalized Navier-Stokes equations with half Laplacian. Therefore with convex integration scheme we obtained such stationary weak solutions, which is not yet realizable in the case of classical 3D Navier-Stokes equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01494 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Three dimensional stationary solutions of the Electron MHD equations Peng, Qirui Analysis of PDEs The goal of this paper is to construct non-trivial steady-state weak solutions of the three dimensional Electron Magnetohydrodynamics equations in the class of $H^s(\mathbb T^3)$ for some small $s > 0$. By exploiting the formulation of the stationary EMHD equations one can treat them as generalized Navier-Stokes equations with half Laplacian. Therefore with convex integration scheme we obtained such stationary weak solutions, which is not yet realizable in the case of classical 3D Navier-Stokes equations. |
| title | Three dimensional stationary solutions of the Electron MHD equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.01494 |