Mean-Square Approximation of Navier-Stokes Equations with Additive Noise in Vorticity-Velocity Formulation

We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions in the vorticity-velocity formulation. The approximation is based on freezing velocity subintervals resulting linear parabolic for vorticity. Probabilistic representations solutions these are given. At each step, expressed via vorticity using formula corresponding to Biot--Savart-type law. show that divergent free and first order. results extended two-dimensional stochastic additive noise, where, particular, we prove mean-square convergence order approximation.