Existence of martingale solutions for stochastic flocking models with local alignment

Arnaud Debussche (1) , Angelo Rosello (2, 1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 MINGUS - Multi-scale numerical geometric schemes

We establish the existence of martingale solutions to a class of stochastic conservation equations. The underlying models correspond to random perturbations of kinetic models for collective motion such as the Cucker-Smale and Motsch-Tadmor models. By regularizing the coefficients, we first construct approximate solutions obtained as the mean-field limit of the corresponding particle systems. We then establish the compactness in law of this family of solutions by relying on a stochastic averaging lemma. This extends the results obtained by Karper, Mellet and Trivisa in the deterministic case.

Mots clés: Stochastic partial differential equations; Mean-field limits; Collective motion

Domaines: Probabilités [math.PR]

Arnaud Debussche, Angelo Rosello. Existence of martingale solutions for stochastic flocking models with local alignment. Stochastics and Partial Differential Equations: Analysis and Computations, 2022, ⟨10.1007/s40072-022-00259-5⟩. ⟨hal-02888169⟩