Error analysis for 3D Navier--Stokes equations with additive noise

Soumya Ranjan Behera; Dominic Breit; Abhishek Chaudhary

Error analysis for 3D Navier--Stokes equations with additive noise

Numerical Analysis 2026-07-10 v1 Analysis of PDEs Probability

Authors: Soumya Ranjan Behera , Dominic Breit , Abhishek Chaudhary

Abstract

We consider the three-dimensional stochastic Navier--Stokes equations with additive stochastic forcing. We study temporal discretizations based on a semi-implicit Euler as well as a Crank-Nicolson scheme. We prove that locally in time the former converges with rate 1 while the latter converges with rate 3/2. These theoretical results are confirmed by extensive numerical simulations. To the best of our knowledge this is the first time that numerical simulations for the three-dimensional stochastic Navier--Stokes equations have been performed.

Cite

@article{arxiv.2607.09926,
  title  = {Error analysis for 3D Navier--Stokes equations with additive noise},
  author = {Soumya Ranjan Behera and Dominic Breit and Abhishek Chaudhary},
  journal= {arXiv preprint arXiv:2607.09926},
  year   = {2026}
}