  A slender-jet model for the pinching of a liquid column is considered in the
limit of vanishing viscosity. We find the model to develop a singularity in the
gradients of the local radius and the velocity at a finite thread radius, so it
does not describe breakup. However, the observed steepening of the profile
corresponds to experiments and simulations with fluids at low viscosity. The
singularity has similarity form, which we compute analytically. The result
agrees well with numerical simulations of the model equations.
