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SUMMARY:Propagation of chaos towards Navier-Stokes for stochastic system o
 f 2D vortices - Maxime Hauray (Université de Provence\, Marseille)
DTSTART:20130218T150000Z
DTEND:20130218T160000Z
UID:TALK41956@talks.cam.ac.uk
CONTACT:Prof. Clément Mouhot
DESCRIPTION:We consider here a system of N vortices interacting between th
 emselves via the Biot-Savard law\, and driven by N independent Brownian mo
 tion.\nOsada showed in 1985 that if the viscosity is sufficiently strong\,
  if the initial vorticity is bounded\, then (full or trajectorial) propaga
 tion of chaos holds for that system\, towards the expected non-linear SDE.
 \nIn particular\, the empirical measures associated to our vortices system
  converges in law towards the unique (under appropriate a priori assumptio
 ns) solution of the vorticity equation. After a short discussion about the
  interest of such model\, we will present a result obtained in collaborati
 on with Nicolas Fournier and Stéphane Mischler\, which extends the result
  of Osada to any positive vorticity\, any initial condition with finite en
 tropy\, and also provide a stronger convergence result: 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
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