Awaiting verificationMathematics, Analysis of PDEsSubmitted 31 Aug 2026

Low Regularity Norm Inflation of Axisymmetric Hall Magnetohydrodynamics in Sobolev Space

10.48550/arxiv.2608.06730 arxiv v1 ↗Published 7 Aug 2026

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

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