  We consider a fluctuating superconductor in the vicinity of the transition
temperature, $T_c$. The fluctuation shear viscosity is calculated. In two
dimensions, the leading correction to viscosity is negative and scales as
$\delta \eta(T) \propto \ln(T-T_c)$. Critical hydrodynamics of the fluctuating
superconductor involves two fluids -- a fluid of fluctuating pairs and a
quasiparticle fluid of single-electron excitations. The pair viscosity
(Aslamazov-Larkin) term is shown to be zero. The (density of states) correction
to viscosity of single-electron excitations is negative, which is due to
fluctuating pairing that results in a reduction of electron density. Scattering
of electrons off of the fluctuations gives rise to an enhanced quasiparticle
scattering and another (Maki-Thomson) negative correction to viscosity. Our
results suggest that fluctuating superconductors provide a promising platform
to investigate low-viscosity electronic media and may potentially host
fermionic/electronic turbulence. Some experimental probes of two-fluid critical
hydrodynamics are proposed such as time-of-flight measurement of turbulent
energy cascades in critical cold atom superfluids and magnetic dynamos in
three-dimensional fluctuating superconductors.
