Stochastic 3D Leray- α model with fractional dissipation

In this paper, we establish the global well-posedness of the stochastic 3D Leray- α model with general fractional dissipation driven by multiplicative noise. This model is the stochastic 3D Navier-Stokes equations regularized through a smoothing kernel of order θ 1 in the nonlinear term and the θ 2 -fractional Laplacian. In the case of θ 1 ⩾ 0 and θ 2 > 0 with θ _1 + θ _2⩾5 4 , we prove the global existence and uniqueness of strong solutions. The main results not only cover many existing works in the deterministic cases, but also generalize some known results of stochastic models such as the stochastic hyperviscous Navier-Stokes equations and classical stochastic 3D Leray- α model as the special cases.