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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Control in fluid mechanics and boundary layers - J
ean-Michel Coron (Université Pierre et Marie Curie
Paris)
DTSTART;TZID=Europe/London:20220107T141000
DTEND;TZID=Europe/London:20220107T151000
UID:TALK166444AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/166444
DESCRIPTION:A control system is a dynamical system on which on
e can act thanks to what is called the control. Fo
r example\, in a car\, one can turn the steering w
heel\, press the accelerator pedal etc. These are
the control(s). One of the main problems in contro
l theory is the controllability problem. One start
s from a given situation and there is a given targ
et. The controllability problem is to see if\, by
using some suitable controls depending on time\, t
he given situation and target\, one can move from
the given situation to the target. We study this p
roblem with a special emphasis on the case where t
he nonlinearities play a crucial role. In finite d
imension in this case a key tool is the use of ite
rated Lie brackets as shown in particular by the R
ashevski-Chow theorem. This key tool gives also im
portant results for some control systems modelled
by means of partial differential equations. Howeve
r we do not know how to use it for many other cont
rol systems modelled by means partial differential
equations. We present methods to avoid the use of
iterated Lie brackets for the control in fluid me
chanics (Euler and Navier-Stokes equations of inco
mpressible fluids\, shallow water equations). A sp
ecial emphasis is put on the problem created by bo
undary layers.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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