The Quarterly Journal of Mechanics and Applied Mathematics · 1994 · 43 citations · 0 references
EngineeringAerospace EngineeringAerodynamicsComputational Fluid DynamicsFluid DynamicsBoundary ConditionsBoundary Layer FlowBoundary LayersBoundary-layer TheoryFlow StabilityMoving Boundary ProblemsFree-surface Boundary Conditions
A special case of the Stefan model for the evolution of zero surface tension Hele-Shaw free-boundary problems is presented. The model relies on allowing the conformal map to have singularities or zeros of its derivatives, thereby generating slits in the physical free boundary. A further possible mechanism for slit initiation is based on Schwartz function formulation. It is concluded that slit mappings are extremal univalent functions which lie naturally on the border between overlapping and non-overlapping maps.