Generalizations of Kadanoff's solution of the Saffman-Taylor problem in a wedge

Details Generalizations of Kadanoff's solution of the Saffman-Taylor problem in a wedge Generalizations of Kadanoff's solution of the Saffman-Taylor problem in a wedge

2005-08-05

arxiv.org/abs/physics/0508039v1

Physics

Fluid Dynamics

9 pages, 7 figures

Scientific paper

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 by Kadanoff.

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