On a Saffman–Taylor problem in an infinite wedge

Abstract

We consider a zero-surface-tension two-dimensional Hele–Shaw flow in an infinite wedge. There exists a self-similar interface evolution in this wedge, an analogue of the famous Saffman–Taylor finger in a channel, exact shape of which has been given by Kadanoff. One of the main features of this evolution is its infinite time of existence and stability for the Hadamard ill-posed problem. We derive several exact solutions existing infinitely by generalizing and perturbing the one given by Kadanoff.