Uniform approximation of 2$d$ Navier-Stokes equation by stochastic interacting particle systems

Franco Flandoli (1) , Christian Olivera (2) , Marielle Simon (3)

1 DMA - Dipartimento di Matematica Applicata [Pisa]
2 IMECC - Instituto de Matemática, Estatística e Computação Científica [Brésil]
3 Paradyse - Systèmes de particules et systèmes dynamiques

We consider an interacting particle system modeled as a system of $N$ stochastic differential equations driven by Brownian motions. We prove that the (mollified) empirical process converges, uniformly in time and space variables, to the solution of the two-dimensional Navier-Stokes equation written in vorticity form. The proofs follow a semigroup approach.

Mots clés: Moderatly interacting particle system; 2d Navier-Stokes equation; Vorticity equation; Analytic semigroup; Stochastic differential equations

Domaines: Probabilités [math.PR]

Franco Flandoli, Christian Olivera, Marielle Simon. Uniform approximation of 2$d$ Navier-Stokes equation by stochastic interacting particle systems. SIAM Journal on Mathematical Analysis, 2020, 52 (6), ⟨10.1137/20M1328993⟩. ⟨hal-02529632v2⟩