Computing finite-time singularities in interfacial flows

Finite-time singularities occurring in mathematical models of free-surface flows indicate that important qualitative changes are taking place; for problems in solid and fluid mechanics this includes topological transitions-blow-up and pinch-off. For many problems, the dynamics leading to the formation of such singularities are described by self-similar solutions of the governing nonlinear partial differential equations. We present an analytical and numerical study of these similarity solutions and discuss their stability.