Interface singularities for the Euler equations
Duration: 54 mins 40 secs
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| Description: |
Shkoller, S (University of Oxford)
Wednesday 23 July 2014, 14:00-14:45 |
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| Created: | 2014-07-25 15:13 |
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| Collection: | Theory of Water Waves |
| Publisher: | Isaac Newton Institute |
| Copyright: | Shkoller, S |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | In fluid dynamics, a "splash" singularity occurs when a locally smooth interface self-intersects in finite-time. It is now well-known that solutions to the water waves equations (and a host of other one-phase fluid interface models) has a finite-time splash singularity. By means of elementary arguments, we prove that such a singularity cannot occur in finite-time for vortex sheet evolution (or two-fluid interfaces). This means that the evolving interface must lose regularity prior to self-intersection. We give a proof by contradiction: we assume that such a singularity does indeed occur in finite-time. Based on this assumption, we find precise blow-up rates for the components of the velocity gradient which, in turn, allows us to characterize the geometry of the evolving interface just prior to self-intersection. The constraints on the geometry then lead to an impossible outcome, giving the contradiction. This is joint work D. Coutand. |
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