Abstract: We first show that the water-waves system is locally well-posed in a class of weighted Sobolev spaces
that allow for interfaces with angled-crests. These singularities are not rigid, i.e. the angle generically
changes with time. Using the characterization of the asymptotic behavior of the fluid near the corner tip,
we then show that there exist initial data for which the fluid velocity blows-up in finite time, while the
opening angle itself converges to $pi/2$.