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SUMMARY:Control in fluid mechanics and boundary layers - Jean-Michel Coron
  (Université Pierre et Marie Curie Paris)
DTSTART:20220107T141000Z
DTEND:20220107T151000Z
UID:TALK166444@talks.cam.ac.uk
DESCRIPTION:A control system is a dynamical system on which one can act th
 anks to what is called the control. For example\, in a car\, one can turn 
 the steering wheel\, press the accelerator pedal etc. These are the contro
 l(s). One of the main problems in control theory is the controllability pr
 oblem. One starts from a given situation and there is a given target. The 
 controllability problem is to see if\, by using some suitable controls dep
 ending on time\, the given situation and target\, one can move from the gi
 ven situation to the target. We study this problem with a special emphasis
  on the case where the nonlinearities play a crucial role. In finite dimen
 sion in this case a key tool is the use of iterated Lie brackets as shown 
 in particular by the Rashevski-Chow theorem. This key tool gives also impo
 rtant results for some control systems modelled by means of partial differ
 ential equations. However we do not know how to use it for many other cont
 rol systems modelled by means partial differential equations. We present m
 ethods to avoid the use of iterated Lie brackets for the control in fluid 
 mechanics (Euler and Navier-Stokes equations of incompressible fluids\, sh
 allow water equations). A special emphasis is put on the problem created b
 y boundary layers.
LOCATION:Seminar Room 1\, Newton Institute
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