Magnetic norm inflation at the $\ell^1$ Besov endpoint for viscous non-resistive incompressible MHD

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 construc