Singularities in droplet pinching with vanishing viscosity

A slender-jet model for the pinching of a liquid column is considered in th e 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 ra dius, so it does not describe breakup. However, the observed steepening of the pro le corresponds to experiments and simulations with fluids at low vi scosity. The singularity has a self-similar form, which we compute analytic ally. The result agrees well with numerical simulations of the model equati ons.