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

LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
Abstract : 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.
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Cited literature [33 references]

https://hal.inria.fr/hal-02529632
Contributor : Marielle Simon <>
Submitted on : Friday, October 16, 2020 - 9:28:13 AM
Last modification on : Thursday, October 29, 2020 - 1:56:02 PM

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### Identifiers

• HAL Id : hal-02529632, version 2
• ARXIV : 2004.00458

### Citation

Franco Flandoli, Christian Olivera, Marielle Simon. Uniform approximation of 2$d$ Navier-Stokes equation by stochastic interacting particle systems. 2020. ⟨hal-02529632v2⟩

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