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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2411.00120 |
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| _version_ | 1866908841642295296 |
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| author | Dai, Mimi |
| author_facet | Dai, Mimi |
| contents | We consider the electron magnetohydrodynamics (MHD) in the context where the 3D magnetic field depends only on the two horizontal plane variables. In particular, the magnetic field takes the form $B=\nabla\times (a\vec e_z)+b\vec e_z$ with $a=a(x,y)$ and $b=b(x,y)$. Initial data $(a_0,b_0)$ is constructed in the Sobolev space $H^β\times H^{β-1}$ with $1<β<4$ such that the solution to this electron MHD system either escapes the space or develops norm inflation in $\dot H^β\times \dot H^{β-1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00120 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ill-posedness of $2\frac12$D electron MHD Dai, Mimi Analysis of PDEs 35Q35, 76E25, 76W05 We consider the electron magnetohydrodynamics (MHD) in the context where the 3D magnetic field depends only on the two horizontal plane variables. In particular, the magnetic field takes the form $B=\nabla\times (a\vec e_z)+b\vec e_z$ with $a=a(x,y)$ and $b=b(x,y)$. Initial data $(a_0,b_0)$ is constructed in the Sobolev space $H^β\times H^{β-1}$ with $1<β<4$ such that the solution to this electron MHD system either escapes the space or develops norm inflation in $\dot H^β\times \dot H^{β-1}$. |
| title | Ill-posedness of $2\frac12$D electron MHD |
| topic | Analysis of PDEs 35Q35, 76E25, 76W05 |
| url | https://arxiv.org/abs/2411.00120 |