Solving the Dirichlet problem for Navier-Stokes equations by probabilistic approach

Abstract

We construct a number of layer methods for Navier-Stokes equations (NSEs) with no-slip boundary conditions. The methods are obtained using probabilistic representations of solutions to NSEs and exploiting ideas of the weak sense numerical integration of stochastic differential equations. Despite their probabilistic nature, the proposed methods are nevertheless deterministic. © 2011 Springer Science + Business Media B.V.