Date(s) : 03/07/2018 iCal
11 h 00 min - 12 h 00 min
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 .
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