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

摘要

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 all 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.