Non-Trivial Self-Similar Extinction Solutions for a 3D Hele–Shaw Suction Problem

Abstract

We show the existence of noncircular, self-similar solutions to the three-dimensional Hele–Shaw suction problem with surface tension regularisation up to complete extinction. In an appropriate scaling, these solutions are found as bifurcation solutions to a nonlocal elliptic equation of order three. The bifurcation parameter is the ratio of the suction speed and the surface tension coefficient.