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CATEGORIES:Partial Differential Equations seminar
SUMMARY:Propagation of chaos towards Navier-Stokes for sto
chastic system of 2D vortices - Maxime Hauray (Uni
versité de Provence\, Marseille)
DTSTART;TZID=Europe/London:20130218T150000
DTEND;TZID=Europe/London:20130218T160000
UID:TALK41956AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/41956
DESCRIPTION:We consider here a system of N vortices interactin
g between themselves via the Biot-Savard law\, and
driven by N independent Brownian motion.\nOsada s
howed in 1985 that if the viscosity is sufficientl
y strong\, if the initial vorticity is bounded\, t
hen (full or trajectorial) propagation of chaos ho
lds for that system\, towards the expected non-lin
ear SDE.\nIn particular\, the empirical measures a
ssociated to our vortices system converges in law
towards the unique (under appropriate a priori ass
umptions) solution of the vorticity equation. Afte
r a short discussion about the interest of such mo
del\, we will present a result obtained in collabo
ration with Nicolas Fournier and Stéphane Mischler
\, which extends the result of Osada to any positi
ve vorticity\, any initial condition with finite e
ntropy\, and also provide a stronger convergence r
esult: the propagation of chaos at fixed times is
entropic. The proof also relies on very different
arguments\, that we shall present if time permits.
LOCATION:CMS\, MR11
CONTACT:Prof. Clément Mouhot
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