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SUMMARY:Uniform in Time Propagation of Chaos for the 2D Vortex Model
DTSTART:20231012T093000Z
DTEND:20231012T100000Z
DTSTAMP:20240919T152600Z
UID:indico-event-10681@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Pierre Le Bris (IHES)\n\nWe are interested in a syst
em of particles in singular mean-field interaction and wish to prove that\
, as the number of particles goes to infinity\, two given particles within
that system become « more and more » independent\, a phenomenon known a
s propagation of chaos. The interaction we will focus on comes from the Bi
ot-Savart kernel\, for which the nonlinear limit of the particle system sa
tisfies the vorticity equation\, arising from the 2D incompressible Navier
-Stokes system. We build upon a recent work of P.-E. Jabin and Z. Wang to
obtain a uniform in time convergence. The approach consists in computing t
he time evolution of the relative entropy of the joint law of the particle
system with respect to the nonlinear limit. We prove time-uniform bounds
on the limit\, as well as a logarithmic Sobolev inequality. From the latte
r\, the Fisher information appearing in the entropy dissipation yields a c
ontrol on the relative entropy itself\, inducing the time uniformity. This
is joint work with A. Guillin and P. Monmarché.\n\nhttps://indico.math.c
nrs.fr/event/10681/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/10681/
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