### Abstract

Recent work [Phys. Fluids 10, 2701 (1998)] has shown that for Hele-Shaw flows sufficiently near a finite-time pinching singularity, there is a breakdown of the leading-order solutions perturbative in a small parameter ∈ controlling the large-scale dynamics. To elucidate the nature of this breakdown we study the structure of these solutions at higher order. We find a finite radius of convergence that yields a new length scale exponentially small in ∈. That length scale defines a ball in space and time, centered around the incipient singularity, inside of which perturbation theory fails. Implications of these results for a possible matching of outer solutions to inner scaling solutions are discussed.

Original language | English (US) |
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Pages (from-to) | 2809-2811 |

Number of pages | 3 |

Journal | Physics of Fluids |

Volume | 11 |

Issue number | 10 |

DOIs | |

State | Published - Oct 1999 |

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### ASJC Scopus subject areas

- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes

### Cite this

*Physics of Fluids*,

*11*(10), 2809-2811. https://doi.org/10.1063/1.870139