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Quantitative particle approximations of stochastic 2D Navier-Stokes equation

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arxiv 2402.02336 v1 pith:VX2PXJGS submitted 2024-02-04 math.PR math.AP

Yufei Shao , Xianliang Zhao This is my paper · ORCID
classification math.PRmath.AP
keywords stochasticentropyequationnavier-stokesnoiserelativedimensionalenvironmental
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In this article, we investigate an interacting particle system featuring random intensities, individual noise, and environmental noise, commonly referred to as stochastic point vortex model. The model serves as an approximation for the stochastic 2-dimensional Navier-Stokes equation. We establish a quantitative mean-field convergence for the stochastic 2-dimensional Navier-Stokes equation in the form of relative entropy. To address challenges posed by environmental noise, random intensities, and singular kernel, we compare relative entropy for conditional distributions, employing technology of disintegration and the relative entropy method developed by Jabin and Wang in [JW18].

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Convergence rate for Fluctuations of mean field interacting diffusion and application to 2D viscous Vortex model and Coulomb potential

    math.PR 2025-09 conditional novelty 8.0 of 10

    First quantitative convergence rate for mean-field fluctuation processes: 1/√N for regular drifts, with weaker rates for singular vortex and Coulomb kernels.

  2. The fluctuation behaviour of the stochastic point vortex model with common noise

    math.PR 2025-01 conditional novelty 6.0 of 10

    The fluctuation process of the stochastic point vortex model with common noise converges in distribution to the unique strong solution of a linear fluctuation SPDE with multiplicative transport noise and a conditional...

  3. Quantitative particle approximation of nonlinear stochastic Fokker-Planck equations with singular kernel

    math.PR 2024-12 conditional novelty 6.0 of 10

    The paper derives explicit N^{-κ} error bounds for the mollified empirical measure of moderately interacting particles with common noise, and proves local strong well-posedness of the limiting stochastic Fokker-Planck...

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