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

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...

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Bibliographic Details
Published in:SIAM journal on mathematical analysis 2020, Vol.52 (6)
Main Authors: Flandoli, Franco, Olivera, Christian, Simon, Marielle
Format: Article
Language:English
Subjects:
Mathematics
Probability
Online Access:Get full text
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Summary: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.
ISSN:0036-1410
DOI:10.1137/20M1328993