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SUMMARY:Rapid convergence to quasi-stationary states for the 2D Navier-Sto
 kes equation - Margaret Beck (Heriot-Watt)
DTSTART:20120514T150000Z
DTEND:20120514T160000Z
UID:TALK37438@talks.cam.ac.uk
CONTACT:Jonathan Ben-Artzi
DESCRIPTION:Quasi-stationary\, or metastable\, states play an important ro
 le in two-dimensional turbulent fluid flows\nwhere they often emerge on ti
 me-scales much shorter than the viscous time scale\, and then dominate the
  dynamics for very long time intervals. We give a dynamical systems explan
 ation of the metastability of an explicit family of solutions\, referred t
 o as bar states\, of the two-dimensional incompressible Navier-Stokes equa
 tion on the torus.  These states are physically relevant because they are 
 associated with certain maximum entropy solutions of the Euler equations\,
  and they have been observed in a variety of settings. Using the so-called
  hypocoercive properties of the linearized operator\, we show that there i
 s an invariant subspace in which there is fast decay. Thus\, we provide ri
 gorous justification for the existence of multiple time-scales and for the
  role that stationary solutions of the Euler equations play in serving as 
 metastable states. This is joint work with C. Eugene Wayne (Boston Univers
 ity).
LOCATION:CMS\, MR11
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