  It is well known that the viscosity of a homogeneous electron liquid diverges
in the limits of zero frequency and zero temperature. A nanojunction breaks
translational invariance and necessarily cuts off this divergence. However, the
estimate of the ensuing viscosity is far from trivial. Here, we propose an
approach based on a Kramers-Kr\"onig dispersion relation, which connects the
zero-frequency viscosity, $\eta(0)$, to the high-frequency shear modulus,
$\mu_{\infty}$, of the electron liquid via $\eta(0) =\mu_{\infty} \tau$, with
$\tau$ the junction-specific momentum relaxation time. By making use of a
simple formula derived from time-dependent current-density functional theory we
then estimate the many-body contributions to the resistance for an integrable
junction potential and find that these viscous effects may be much larger than
previously suggested for junctions of low conductance.
