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SUMMARY:Applications of optimization and optimal control to some fundament
 al problems in mathematical fluid dynamics - Charlie Doering (University o
 f Michigan)
DTSTART:20170503T120000Z
DTEND:20170503T130000Z
UID:TALK72341@talks.cam.ac.uk
CONTACT:Doris Allen
DESCRIPTION:Optimization and optimal dynamical control are used to investi
 gate the accuracy of analytical estimates for solutions of some basic nonl
 inear partial differential equations of mathematical hydrodynamics. Even t
 hough many mathematical estimates are demonstrably sharp\, the result of a
  sequence of applications of such estimates need not be sharp leaving unce
 rtainty in the ultimate result of the analysis.  We examine the classical 
 analysis for enstrophy and palinstrophy amplification in Burgers’ and th
 e Navier-Stokes equations and discover that the best known instantaneous g
 rowth rates estimates are indeed sharp. Integrating the estimates in time\
 , however\, may (as in the 2D Navier-Stokes case) but does not always (as 
 in the Burgers case) produce sharp estimates in which case optimal control
  techniques must be brought to bear to determine the actual extreme behavi
 or of the nonlinear dynamics. The question of 3D Navier-Stokes regularity 
 remains unresolved although work is in progress to apply these tools to th
 e challenge.
LOCATION:MR5\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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