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.
Acknowledgements
The authors Irina Markina and Alexander Vasil’ev were supported by the grant of the University of Bergen (Norway) and the grant of the Norwegian Research Council #177355; the author Rodrigo Meneses was partially supported by Project Fondecyt #1040333, and UTFSM #12.05.23 (Chile).