Convergence for a Splitting-Up Scheme for the 3D Stochastic Navier-Stokes-α Model

Abstract

We propose and analyze a splitting-up scheme for the numerical approximation of the 3D stochastic Navier-Stokes-α model. We prove the convergence of the scheme to the unique variational solution of the 3D stochastic Navier-Stokes-α model when the time step tends to zero.

Keywords:

• Compactness
• Navier-Stokes-α model
• Splitting-up scheme
• Tightness

Mathematics Subject Classification:

• 35R60, 35Q30, 60H15, 60H30, 60H35