On the regularity of Lagrangian trajectories in the 3D Navier-Stokes flow
Duration: 24 mins 9 secs
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| Description: |
Sadowski, W (University of Warsaw)
Thursday 26 July 2012, 12:10-12:30 |
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| Created: | 2012-07-31 17:27 |
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| Collection: | Topological Dynamics in the Physical and Biological Sciences |
| Publisher: | Isaac Newton Institute |
| Copyright: | Sadowski, W |
| 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: | The paper considers suitable weak solutions of the 3D Navier-Stokes equations. Such solutions are defined globally in time and satisfy local energy inequality but they are not known to be regular. However, as it was proved in a seminal paper by Caffarelli, Kohn and Nirenberg, their singular set S in space-time must be ``rather small'' as its one-dimensional parabolic Hausdorff measure is zero. In the paper we use this fact to prove that almost all Lagrangian trajectories corresponding to a given suitable weak solution avoid a singular set in space-time. As a result for almost all initial conditions in the domain of the flow Lagrangian trajectories generated by a suitable weak solution are unique and C^1 functions of time. This is a joint work with James C. Robinson. |
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