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CATEGORIES:Fluid Mechanics (DAMTP)
SUMMARY:Applications of optimization and optimal control t
o some fundamental problems in mathematical fluid
dynamics - Charlie Doering (University of Michigan
)
DTSTART;TZID=Europe/London:20170503T130000
DTEND;TZID=Europe/London:20170503T140000
UID:TALK72341AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/72341
DESCRIPTION:Optimization and optimal dynamical control are use
d to investigate the accuracy of analytical estima
tes for solutions of some basic nonlinear partial
differential equations of mathematical hydrodynami
cs. Even though many mathematical estimates are de
monstrably sharp\, the result of a sequence of app
lications of such estimates need not be sharp leav
ing uncertainty in the ultimate result of the anal
ysis. We examine the classical analysis for enstr
ophy and palinstrophy amplification in Burgersâ€™ an
d the Navier-Stokes equations and discover that th
e best known instantaneous growth rates estimates
are indeed sharp. Integrating the estimates in tim
e\, however\, may (as in the 2D Navier-Stokes case
) but does not always (as in the Burgers case) pro
duce sharp estimates in which case optimal control
techniques must be brought to bear to determine t
he actual extreme behavior of the nonlinear dynami
cs. The question of 3D Navier-Stokes regularity re
mains unresolved although work is in progress to a
pply these tools to the challenge.
LOCATION:MR5\, Centre for Mathematical Sciences\, Wilberfor
ce Road\, Cambridge
CONTACT:Doris Allen
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