Abstract
We provide numerical and analytic evidence for the formation of a singularity driven only by surface tension in the mathematical model describing a two-dimensional Hele–Shaw cell with no air injection. Constantin and Pugh have proved that no such singularity is possible if the initial shape is close to a circle; thus we show that their result is not true in general. Our evidence takes the form of direct numerical simulation of the full problem, including a careful assessment of the effects of limited spatial resolution, and comparison of the full problem with the lubrication approximation.
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