Domain of convergence of perturbative solutions for Hele-Shaw flow near interface collapse

Adriana J. Pesci, Raymond E. Goldstein, Michael Shelley

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)2809-2811
Number of pages3
JournalPhysics of Fluids
Volume11
Issue number10
StatePublished - Oct 1999

Fingerprint

breakdown
Fluids
balls
perturbation theory
scaling
radii
fluids

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

Pesci, A. J., Goldstein, R. E., & Shelley, M. (1999). Domain of convergence of perturbative solutions for Hele-Shaw flow near interface collapse. Physics of Fluids, 11(10), 2809-2811.

Domain of convergence of perturbative solutions for Hele-Shaw flow near interface collapse. / Pesci, Adriana J.; Goldstein, Raymond E.; Shelley, Michael.

In: Physics of Fluids, Vol. 11, No. 10, 10.1999, p. 2809-2811.

Research output: Contribution to journalArticle

Pesci, AJ, Goldstein, RE & Shelley, M 1999, 'Domain of convergence of perturbative solutions for Hele-Shaw flow near interface collapse', Physics of Fluids, vol. 11, no. 10, pp. 2809-2811.
Pesci, Adriana J. ; Goldstein, Raymond E. ; Shelley, Michael. / Domain of convergence of perturbative solutions for Hele-Shaw flow near interface collapse. In: Physics of Fluids. 1999 ; Vol. 11, No. 10. pp. 2809-2811.
@article{4d14c019afa645ae8f3a6d4a11e9a9a6,
title = "Domain of convergence of perturbative solutions for Hele-Shaw flow near interface collapse",
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.",
author = "Pesci, {Adriana J.} and Goldstein, {Raymond E.} and Michael Shelley",
year = "1999",
month = "10",
language = "English (US)",
volume = "11",
pages = "2809--2811",
journal = "Physics of Fluids",
issn = "1070-6631",
publisher = "American Institute of Physics Publising LLC",
number = "10",

}

TY - JOUR

T1 - Domain of convergence of perturbative solutions for Hele-Shaw flow near interface collapse

AU - Pesci, Adriana J.

AU - Goldstein, Raymond E.

AU - Shelley, Michael

PY - 1999/10

Y1 - 1999/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0000107553&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000107553&partnerID=8YFLogxK

M3 - Article

VL - 11

SP - 2809

EP - 2811

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 10

ER -