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

Date:
Thursday 26th July 2012 - 12:10 to 12:30
Venue:
INI Seminar Room 1
Session Chair:
Andrew Gilbert
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.
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
Presentation Material: