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On the regularity of Lagrangian trajectories in the 3D Navier-Stokes flow

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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.

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Average on weekdays: 9181.2773386 kWh BMSLecture Theatre Queen Mary University of London (Math Building Lecture Theatre)

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