The motion of a viscous filament in a porous medium or Hele-Shaw cell: a physical realisation of the Cauchy-Riemann Equations
We consider the motion of a thin filament of viscous fluid in a Hele-Shaw cell. The appropriate thin film analysis and use of Lagrangian variables leads to the Cauchy-Riemann system in a surprisingly direct way. We illustrate the inherent ill-posedness of these equations in various contexts.
Asıl Yazarlar: | , |
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Materyal Türü: | Journal article |
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2005
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_version_ | 1826281243723956224 |
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author | Farmer, C Howison, S |
author_facet | Farmer, C Howison, S |
author_sort | Farmer, C |
collection | OXFORD |
description | We consider the motion of a thin filament of viscous fluid in a Hele-Shaw cell. The appropriate thin film analysis and use of Lagrangian variables leads to the Cauchy-Riemann system in a surprisingly direct way. We illustrate the inherent ill-posedness of these equations in various contexts. |
first_indexed | 2024-03-07T00:25:52Z |
format | Journal article |
id | oxford-uuid:7e1bb7fc-b627-4894-b2d8-a8c9ee7c01ce |
institution | University of Oxford |
last_indexed | 2024-03-07T00:25:52Z |
publishDate | 2005 |
record_format | dspace |
spelling | oxford-uuid:7e1bb7fc-b627-4894-b2d8-a8c9ee7c01ce2022-03-26T21:08:10ZThe motion of a viscous filament in a porous medium or Hele-Shaw cell: a physical realisation of the Cauchy-Riemann EquationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7e1bb7fc-b627-4894-b2d8-a8c9ee7c01ceMathematical Institute - ePrints2005Farmer, CHowison, SWe consider the motion of a thin filament of viscous fluid in a Hele-Shaw cell. The appropriate thin film analysis and use of Lagrangian variables leads to the Cauchy-Riemann system in a surprisingly direct way. We illustrate the inherent ill-posedness of these equations in various contexts. |
spellingShingle | Farmer, C Howison, S The motion of a viscous filament in a porous medium or Hele-Shaw cell: a physical realisation of the Cauchy-Riemann Equations |
title | The motion of a viscous filament in a porous medium or Hele-Shaw cell: a physical realisation of the Cauchy-Riemann Equations |
title_full | The motion of a viscous filament in a porous medium or Hele-Shaw cell: a physical realisation of the Cauchy-Riemann Equations |
title_fullStr | The motion of a viscous filament in a porous medium or Hele-Shaw cell: a physical realisation of the Cauchy-Riemann Equations |
title_full_unstemmed | The motion of a viscous filament in a porous medium or Hele-Shaw cell: a physical realisation of the Cauchy-Riemann Equations |
title_short | The motion of a viscous filament in a porous medium or Hele-Shaw cell: a physical realisation of the Cauchy-Riemann Equations |
title_sort | motion of a viscous filament in a porous medium or hele shaw cell a physical realisation of the cauchy riemann equations |
work_keys_str_mv | AT farmerc themotionofaviscousfilamentinaporousmediumorheleshawcellaphysicalrealisationofthecauchyriemannequations AT howisons themotionofaviscousfilamentinaporousmediumorheleshawcellaphysicalrealisationofthecauchyriemannequations AT farmerc motionofaviscousfilamentinaporousmediumorheleshawcellaphysicalrealisationofthecauchyriemannequations AT howisons motionofaviscousfilamentinaporousmediumorheleshawcellaphysicalrealisationofthecauchyriemannequations |