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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On the regularity of Lagrangian trajectories in th
e 3D Navier-Stokes flow - Sadowski\, W (University
of Warsaw)
DTSTART;TZID=Europe/London:20120726T121000
DTEND;TZID=Europe/London:20120726T123000
UID:TALK39072AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/39072
DESCRIPTION:The paper considers suitable weak solutions of the
3D Navier-Stokes equations. Such solutions are de
fined globally in time and satisfy local energy in
equality but they are not known to be regular. How
ever\, as it was proved in a seminal paper by Caff
arelli\, 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 gi
ven suitable weak solution avoid a singular set in
space-time. As a result for almost all initial co
nditions in the domain of the flow Lagrangian traj
ectories 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
CONTACT:Mustapha Amrani
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