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SUMMARY:On the regularity of Lagrangian trajectories in the 3D Navier-Stok
 es flow - Sadowski\, W (University of Warsaw)
DTSTART:20120726T111000Z
DTEND:20120726T113000Z
UID:TALK39072@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The paper considers suitable weak solutions of the 3D Navier-S
 tokes equations. Such solutions are defined globally in time and satisfy l
 ocal energy inequality but they are not known to be regular. However\, as 
 it was proved in a seminal paper by Caffarelli\, Kohn and Nirenberg\, thei
 r singular set S in space-time must be ``rather small'' as its one-dimensi
 onal parabolic Hausdorff measure is zero. In the paper we use this fact to
  prove that almost all Lagrangian trajectories corresponding to a given su
 itable weak solution avoid a singular set in space-time. As a result for a
 lmost all initial conditions in the domain of the flow Lagrangian trajecto
 ries generated by a suitable weak solution are unique and C^1 functions of
  time. This is a joint work with James C. Robinson.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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