Abstract
Free surface flow in a Hele–Shaw cell is considered. It has been known for some time that when the fluid region is contracting, a finite time blow-up can occur, in which a cusp forms in the free surface; the solution does not exist beyond the time of blow-up. Examples are presented of this blow-up, and also of a new process in which a cusp of a different type forms in the free surface, but after which the solution continues to exist. After a transformation of the dependent variable (the pressure) the new cusps are related to permissible singularities in the free boundary of the “obstacle” problem.
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