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Persistence of corners in free boundaries in Hele-Shaw flow. (English) Zbl 0840.76016
Summary: We investigate the movement of free boundaries in the two-dimensional Hele-Shaw problem. By means of the construction of special solutions of self-similar type, we can describe the evolution of free boundary corners in terms of the angle at the corner. In particular, we prove that, in the injection case, while obtuse-angled corners move and smooth out instantaneously, acute-angled corners persist until a (finite) waiting time at which, at least for the special solutions, they suddenly jump into an obtuse angle, precisely the supplement of the original one. The critical values of the angle $$\pi$$ and $$\pi/2$$ are also considered.

MSC:
 76D99 Incompressible viscous fluids