Speaker Affiliation :
Date(s) - 03/07/2018
11 h 00 min - 12 h 00 min
Catégories Pas de Catégories
In this work we deal with the local in time propagation of chaos without cut-off for some two dimensional fractional Keller Segel models. More precisely the diffusion considered here is given by the fractional Laplacian operator −(−∆) ^(a/2) with a ∈ (1, 2) and the singularity of the interaction is of order |x|^(1−α) with α ∈]1, a]. In the case α ∈ (1, a) we prove a complete propagation of chaos result, proving the Γ-l.s.c property of the fractional Fisher information, already known for the classical Fisher information, using a result of . In the fair competition case () a = α, we only prove a convergence/consistency result in a sub-critical mass regime, similarly as the result obtained for the classical Keller-Segel equation in .
 J. Carrillo, V. Calvez, F. Hoffmann. Equilibria of homogeneous functionals in the fair-competition regime Nonlinear Analysis, (2016).
 N. Fournier, B. Jourdain. Stochastic particle approximation of the Keller-Segel equation and two-dimensional generalization of Bessel processes. Accepted at Ann. Appl. Probab.
 N. Fournier, M. Hauray, S. Mischler. Propagation of chaos for the 2D viscous vortex model. J. Eur. Math. Soc., Vol. 16, No 7, 1423-1466, 2014.
 M. Hauray, S. Mischler. On Kac’s chaos and related problems, J. Funct. Anal., Volume 266, P. 60556157,(2014).