## Abstract

Recent numerical evidence suggests that in the Hele-Shaw suction problem with vanishingly small surface tension γ, the free boundary generically approaches the sink in a wedge-like configuration, blow-up occurring when the wedge apex reaches the sink. Sometimes two or more such wedges approach the sink simultaneously. We construct a family of solutions to the zero-surface tension (ZST) problem in which fluid is injected at the (coincident) apices of an arbitrary number N of identical infinite wedges, of arbitrary angle. The time reversed suction problem then models what is observed numerically with non-zero surface tension. We conjecture that (for a given value of N) a particular member of this family of ZST solutions, with special complex plane singularity structure, is selected in the limit γ → 0.

Original language | English (US) |
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Pages (from-to) | 1-37 |

Number of pages | 37 |

Journal | European Journal of Applied Mathematics |

Volume | 15 |

Issue number | 1 |

DOIs | |

State | Published - Feb 2004 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Applied Mathematics