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arXiv · 2608.06730

Low Regularity Norm Inflation of Axisymmetric Hall Magnetohydrodynamics in Sobolev Space

Haoming Zhu
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Abstract

In this paper, we study the axisymmetric Hall magnetohydrodynamics where $u = u^re_r+u^ze_z$ and $B = B^\theta e_\theta$. If there is a smooth solution to the system, we proved that this solution must exhibit norm inflation in $H^{\sigma-1}(\mathbb R^3) \times H^{\sigma}(\mathbb R^3)$ for $1<\sigma<7/2$. If the smooth solution to Hall magnetohydrodynamics is unique, then this also implies a norm inflation in Hall magnetohydrodynamics.

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Haoming Zhu. 2026-08-07. Low Regularity Norm Inflation of Axisymmetric Hall Magnetohydrodynamics in Sobolev Space. https://arxiv.org/abs/2608.06730

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