The 2-D stochastic Keller-Segel particle model : existence and uniqueness

Patrick Cattiaux (1) , Laure Pédèches (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We introduce a stochastic system of interacting particles which is expected to furnish as the number of particles goes to infinity a stochastic approach of the 2-D Keller-Segel model. In this note, we prove existence and some uniqueness for the stochastic model for the parabolic-elliptic Keller-Segel equation, for all regimes under the critical mass. Prior results for existence and weak uniqueness have been very recently obtained by N. Fournier and B. Jourdain [6].

Mots clés: Keller-Segel model; diffusion processes; Bessel processes

Domaines: Probabilités [math.PR]

Patrick Cattiaux, Laure Pédèches. The 2-D stochastic Keller-Segel particle model : existence and uniqueness. 2016. ⟨hal-01263156⟩