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...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.展开更多
文摘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.