  We develop a theory of viscous dissipation in one-dimensional
single-component quantum liquids at low temperatures. Such liquids are
characterized by a single viscosity coefficient, the bulk viscosity. We show
that for a generic interaction between the constituent particles this viscosity
diverges in the zero-temperature limit. In the special case of integrable
models, the viscosity is infinite at any temperature, which can be interpreted
as a breakdown of the hydrodynamic description. Our consideration is applicable
to all single-component Galilean-invariant one-dimensional quantum liquids,
regardless of the statistics of the constituent particles and the interaction
strength.
