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CATEGORIES:Partial Differential Equations seminar
SUMMARY:Rapid convergence to quasi-stationary states for t
he 2D Navier-Stokes equation - Margaret Beck (Heri
ot-Watt)
DTSTART;TZID=Europe/London:20120514T160000
DTEND;TZID=Europe/London:20120514T170000
UID:TALK37438AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/37438
DESCRIPTION:Quasi-stationary\, or metastable\, states play an
important role in two-dimensional turbulent fluid
flows\nwhere they often emerge on time-scales much
shorter than the viscous time scale\, and then do
minate the dynamics for very long time intervals.
We give a dynamical systems explanation of the met
astability of an explicit family of solutions\, re
ferred to as bar states\, of the two-dimensional i
ncompressible Navier-Stokes equation on the torus.
These states are physically relevant because the
y are associated with certain maximum entropy solu
tions of the Euler equations\, and they have been
observed in a variety of settings. Using the so-ca
lled hypocoercive properties of the linearized ope
rator\, we show that there is an invariant subspac
e in which there is fast decay. Thus\, we provide
rigorous justification for the existence of multip
le time-scales and for the role that stationary so
lutions of the Euler equations play in serving as
metastable states. This is joint work with C. Euge
ne Wayne (Boston University).
LOCATION:CMS\, MR11
CONTACT:Jonathan Ben-Artzi
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