= Selective decay bound for magnetic helicity
{title2=$|\dot H|\leq2\mu_0\sqrt{2\eta_mE_BD_B}$}
With the closed-boundary assumptions of the <resistive magnetic-helicity balance>, define the nonnegative resistive <magnetic energy> loss $D_B=\eta_m\int_V|\nabla\times\mathbf B|^2\,dV/\mu_0$. The <Cauchy-Schwarz inequality> gives the displayed bound. Consequently, in a family of fields with bounded $E_B,D_B$ as $\eta_m\to0$, resistive <magnetic helicity> loss tends to zero even when $D_B$ remains finite. This is an absolute conservation estimate; it is not a universal comparison of fractional decay times. For a single <Beltrami field> with $\nabla\times\mathbf B=k\mathbf B$ and no motion, both $E_B$ and $H$ have the same fractional decay rate $2\eta_mk^2$.
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