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arXiv · 2611.01124

Magnetic norm inflation below the velocity regularity threshold for viscous non-resistive MHD

Yinghui Wang
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Abstract

We study viscous, non-resistive magnetohydrodynamics on $\mathbb R^d$, $d\in\{2,3\}$. For every fixed magnetic exponent $s>d/2$ and every velocity exponent $q d/2$. The construction uses a symmetric pair of high-frequency velocity packets and a fixed low-frequency magnetic profile. A Fourier component of their stretching interaction has a fixed sign and gains the power $K^{s-1-q}$ on a short diffusive time scale. Subtracting an exact reference flow and using endpoint Besov estimates controls the full nonlinear remainder. Quantitative higher-order estimates ensure existence through the observation time and yield the uniform smallness of the velocity in the target norm.

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Yinghui Wang. 2026-10-31. Magnetic norm inflation below the velocity regularity threshold for viscous non-resistive MHD. https://arxiv.org/abs/2611.01124

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