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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.

76D99 Incompressible viscous fluids