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CATEGORIES:Fluid Mechanics (DAMTP)
SUMMARY:Dynamic Depletion of Vortex Stretching and Nonline
ar\n Stability of 3D Incompressible Flows -
Tom Hou\, Caltech
DTSTART;TZID=Europe/London:20070615T160000
DTEND;TZID=Europe/London:20070615T170000
UID:TALK6939AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/6939
DESCRIPTION:Whether the 3D incompressible Euler or Navier-Stok
es equations\ncan develop a finite time singularit
y from smooth initial data has been\nan outstandin
g open problem. Here we review some existing compu
tational and theoretical work on possible finite b
low-up of the 3D Euler equations.\nWe show that th
e geometric regularity of vortex filaments\, even
in an extremely localized region\, can lead to dyn
amic depletion of vortex\nstretching\, thus avoid
finite time blowup of the 3D Euler equations. Furt
her\, we perform large scale computations of the 3
D Euler equations\nto re-examine the two slightly
perturbed anti-parallel vortex tubes which is cons
idered as one of the most attractive candidates fo
r a\nfinite time blowup of the 3D Euler equations.
We found that there is tremendous dynamic depleti
on of vortex stretching and the maximum\nvorticity
does not grow faster than double exponential in t
ime. Finally\,\nwe present a new class of solution
s for the 3D Euler and Navier-Stokes\nequations\,
which exhibit very interesting dynamic growth prop
erty. By\nexploiting the special nonlinear structu
re of the equations\, we prove nonlinear stability
and the global regularity of this class of soluti
ons.
LOCATION:MR2\, Centre for Mathematical Sciences
CONTACT:Nigel Peake
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