Hele-shaw free-boundary problems with suction

In the absence of surface tension, the solution of most Hele-Shaw free-boundary problems with suction becomes singular at finite time, say t = t^*, when the free boundary develops a cusp. This paper considers the evolution of the free boundary in the presence of small non-zero surface tension for times slightly greater than t^*; the suggested structure for the free boundary is that of a smooth part together with thin fingers of air which rapidly penetrate the liquid region. © 1988 Oxford University Press.