Irregular morphologies in unstable hele-shaw free-boundary problems

A. A. Lacey, S. D. Howison, J. R. Ockendon, P. Wilmott

Research output: Contribution to journalArticlepeer-review


A model is presented that is intended to describe the evolution of the ill-posed Hele-Shaw suction free-boundary problem at times after that at which 'blow-up' would occur in the absence of surface-tension effects. For small surface tension, it is proposed that the free-boundary morphology consists of thin 'cracks', whose shape and thickness are predicted when appropriate initial data are prescribed. This prediction involves an analytic continuation and the singularities encountered in the construction of the solution are related to those which are known to occur in exact solutions in the absence of surface tension. © 1990 Oxford University Press.

Original languageEnglish
Pages (from-to)387-405
Number of pages19
JournalQuarterly Journal of Mechanics and Applied Mathematics
Issue number3
Publication statusPublished - Aug 1990

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