The spontaneous generation of the singularity in a separating laminar boundary layer

The question whether solutions of the unsteady laminar boundary layer equation may turn singular spontaneously has been in dispute lately. By a case study, here a numerical proof is given that the spontaneous generation of a singularity does indeed occur, thus settling the point. The proof is achieved by abandoning the usual Eulerian boundary layer coordinates in favor of Lagrangian coordinates. The singularity then occurs at a stationary point, the presence of which can be ascertained numerically without ambiguity.