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SUMMARY:Stabilizing unstable flows by coarse mesh observables  and actuato
 rs - a pavement to data assimilation - Edriss Titi (Weizmann Institite &  
 Texas A&M University)
DTSTART:20170601T140000Z
DTEND:20170601T150000Z
UID:TALK71550@talks.cam.ac.uk
CONTACT:6743
DESCRIPTION:One of the main characteristics of infinite-dimensional dissip
 ative evolution equations\, such as the Navier-Stokes equations and reacti
 on-diffusion systems\, is that their long-time dynamics are determined by 
 finitely many parameters -- finite number of determining modes\, nodes\, v
 olume elements and other determining interpolants. In this talk I  will sh
 ow how to explore this finite-dimensional feature\, of the long-time behav
 ior of infinite-dimensional dissipative systems\,  to design finite-dimens
 ional feedback control for stabilizing their solutions.  Moreover\,  based
  on this approach I will also present a data assimilation (downscaling) al
 gorithm for weather and climate predictions employing discrete coarse mesh
  measurements. Notably\, numerical implementation of this algorithm  yield
 s errors that are bounded uniformly in time\; consequently it can be relia
 bly used for  long-time integration and statistics. Finally\, computationa
 l demonstrations implementing this algorithm   will exhibit  that its perf
 ormance remarkably exceeds  what is suggested by the theory.
LOCATION:MR 14\, CMS
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