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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > On the regularity of Lagrangian trajectories in the 3D Navier-Stokes flow

## On the regularity of Lagrangian trajectories in the 3D Navier-Stokes flowAdd to your list(s) Download to your calendar using vCal - Sadowski, W (University of Warsaw)
- Thursday 26 July 2012, 12:10-12:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Topological Dynamics in the Physical and Biological Sciences 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. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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