TY - JOUR T1 - Mean-Square Approximation of Navier-Stokes Equations with Additive Noise in Vorticity-Velocity Formulation AU - Milstein , G.N. AU - Tretyakov , M.V. JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 1 EP - 30 PY - 2020 DA - 2020/10 SN - 14 DO - http://doi.org/10.4208/nmtma.OA-2020-0034 UR - https://global-sci.org/intro/article_detail/nmtma/18325.html KW - Navier-Stokes equations, vorticity, numerical method, stochastic partial differential equations, mean-square convergence. AB -

We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions and additive noise in the vorticity-velocity formulation. The approximation is based on freezing the velocity on time subintervals resulting in a linear stochastic parabolic equation for vorticity. At each time step, the velocity is expressed via vorticity using a formula corresponding to the Biot-Savart-type law. We prove the first mean-square convergence order of the vorticity approximation.