On the regularity of Lagrangian trajectories in the 3D Navier-Stokes flow
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334.99 MB,
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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) |
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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