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

Franco Flandoli; Christian Olivera; Marielle Simon

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arXiv · 2004.00458

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

Franco Flandoli·Christian Olivera·Marielle Simon

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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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Franco Flandoli, Christian Olivera, Marielle Simon. 2020-04-01. Uniform approximation of 2$d$ Navier-Stokes equation by stochastic interacting particle systems. https://arxiv.org/abs/2004.00458

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