Half Strong Ill-Posedness of $2 \frac{1}{2}$D Electron Magnetohydrodynamics with Fractional Resistivity
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912976570679296 |
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| author | Xiaotong Yang Zhu, Haoming |
| author_facet | Xiaotong Yang Zhu, Haoming |
| contents | We study the $2\frac{1}{2}$D electron magnetohydrodynamics (MHD): the electron MHD system that has $3$D magnetic field but is independent of $z$-variable. We establish a "half" strong ill-posedness result in $2\frac{1}{2}$D electron MHD with fractional resistivity $(-Δ)^α$ in the supercritical Sobolev space $H^β\times H^{β-1}$ for $3<β<4-2α$. Specifically, we construct small initial data $(a_0,b_0)$ whose solution develops a norm inflation in $a$ but the norm of $b$ remains small. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20477 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Half Strong Ill-Posedness of $2 \frac{1}{2}$D Electron Magnetohydrodynamics with Fractional Resistivity Xiaotong Yang Zhu, Haoming Analysis of PDEs 35Q35, 76D03, 76E25, 76W05 We study the $2\frac{1}{2}$D electron magnetohydrodynamics (MHD): the electron MHD system that has $3$D magnetic field but is independent of $z$-variable. We establish a "half" strong ill-posedness result in $2\frac{1}{2}$D electron MHD with fractional resistivity $(-Δ)^α$ in the supercritical Sobolev space $H^β\times H^{β-1}$ for $3<β<4-2α$. Specifically, we construct small initial data $(a_0,b_0)$ whose solution develops a norm inflation in $a$ but the norm of $b$ remains small. |
| title | Half Strong Ill-Posedness of $2 \frac{1}{2}$D Electron Magnetohydrodynamics with Fractional Resistivity |
| topic | Analysis of PDEs 35Q35, 76D03, 76E25, 76W05 |
| url | https://arxiv.org/abs/2603.20477 |