Magnetic norm inflation at the $\ell^1$ Besov endpoint for viscous non-resistive incompressible MHD
Year: 2026
Type: preprint
Abstract: We prove magnetic-field norm inflation at the origin for the viscous, non-resistive incompressible magnetohydrodynamic equations on $\R^d$, $d\ge2$, in the endpoint space \[ \dot B^{-1}_{\infty,1}(\R^d)\times \dot B^{0}_{\infty,1}(\R^d). \] For every sufficiently small $\varepsilon>0$, we construct smooth divergence-free initial data $(u_0,b_0)$, with $b_0$ compactly supported and \[ \norm[\dot B^{-1}_{\infty,1}]{u_0} +\norm[\dot B^{0}_{\infty,1}]{b_0}<\varepsilon, \] such that the corresponding classical solution satisfies \[ \norm[\dot B^{0}_{\infty,1}]{b(t_\varepsilon)}>\varepsilon^{-1} \] for some $0
Source: arXiv (Cornell University)
Authors: Ban, Yingzhe, Guo, Boling, Guo, Maotuo
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213407113