= Viscous regularization of the Taylor constraint
{title2=$\mathcal T_L(s)+\mathcal T_\nu(s)=0$}
With small viscosity, the azimuthal cylindrical balance permits <Lorentz force> torque to be cancelled by viscous stress. For ordinary no-slip rotating boundaries an <Ekman layer> gives stress of order $\rho\Omega LU\sqrt E$, larger than the order-$E$ bulk viscous correction at fixed velocity. Thus bounded small-$E$ flows approach a <magnetostrophic Taylor state> but need not satisfy its constraint exactly at finite viscosity. An order-one uncompensated magnetic torque would require a divergent flow as $E\to0$, invalidating the assumed small-inertia balance. Stress-free boundaries remove the leading no-slip friction and require their own torque/regularity conditions.
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