Singularities in Hele-Shaw Flows

We study, analytically and numerically, singularities in an interface flow driven by surface tension and a sink in a two-dimensional Hele--Shaw cell. Our analysis proves that singularity formation is inevitable in generic situations. Our numerical simulations suggest that the Hele--Shaw solution develops singularities via the interface reaching the sink before all the fluid is sucked out. A corner is formed right at the tip of the interface that touches the sink.

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