On the Stochastic 3D Navier-Stokes-α Model of Fluids Turbulence

Abstract

We investigate the stochastic 3D Navier-Stokes-$\alpha$ model which arises in the modelling of turbulent flows of fluids. Our model contains nonlinear forcing terms which do not satisfy the Lipschitz conditions. The adequate notion of solutions is that of probabilistic weak solution. We establish the existence of a such of solution. We also discuss the uniqueness.