Layer methods for Navier-Stokes equations with additive noise

TL;DR

This paper introduces layer methods for solving stochastic Navier-Stokes equations with additive noise, utilizing probabilistic representations and weak numerical integration, with proven convergence and demonstrated numerical effectiveness.

Contribution

The paper develops new layer methods based on probabilistic representations for stochastic Navier-Stokes equations, including convergence analysis and numerical validation.

Findings

Methods show convergence in theoretical analysis.

Numerical experiments confirm effectiveness on model problems.

Approach leverages probabilistic and weak integration techniques.

Abstract

We propose and study a number of layer methods for stochastic Navier-Stokes equations (SNSE) with spatial periodic boundary conditions and additive noise. The methods are constructed using conditional probabilistic representations of solutions to SNSE and exploiting ideas of the weak sense numerical integration of stochastic differential equations. We prove some convergence results for the proposed methods. Results of numerical experiments on two model problems are presented.