Generic solution breakdown in Hele-Shaw flow with a point sink: an open selection problem?
Duration: 53 mins 23 secs
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About this item
| Description: |
Linda Cummings New Jersey Institute of Technology
8 June 2021 – 16:00 to 17:00 |
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| Created: | 2021-06-09 09:26 |
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| Collection: | Applicable resurgent asymptotics: towards a universal theory |
| Publisher: | Isaac Newton Institute for Mathematical Sciences |
| Copyright: | Linda Cummings |
| Language: | eng (English) |
| Abstract: | Brief abstract: Hele-Shaw flow with a free
boundary driven by a point sink almost always breaks down in finite time before all fluid can be removed through the sink. With no surface tension this solution breakdown is typically via 3/2-power cusp formation in the free boundary far from the sink, but accurate numerical results with small positive surface tension suggest that in fact breakdown should occur via a "wedge" of air that enters the sink. A family of zero-surface-tension (similarity) solutions can be constructed that exhibit this local behavior but, as with the well-known Saffman-Taylor finger solutions, the question of what determines the wedge angle for vanishingly small positive surface tension is a challenge. |
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