ON THE BREAKDOWN OF HELE-SHAW SOLUTIONS WITH NONZERO SURFACE-TENSION

In this note, we consider the nonzero surface tension Hele-Shaw proble m in the presence of a sink when the initial fluid domain is bounded. We show that if the geometric center of the initial domain is not at t he sink, either the solution will break down before all the fluid is s ucked out or the fluid domain will eventually become unbounded with a zero area. We do not determine the mechanism of the breakdown. It coul d be caused by topological changes of the fluid domain, by the interfa ce reaching the sink, or perhaps by some other means.