LARGE DEVIATIONS FOR STOCHASTIC 3D LERAY-α MODEL WITH FRACTIONAL DISSIPATION

In this paper we establish the Freidlin-Wentzell's large deviation principle for stochastic 3D Leray-alpha model with general fractional dissipation and small multiplicative noise. This model is the stochastic 3D Navier-Stokes equations regularized through a smoothing kernel of order theta(1) in the nonlinear term and a theta(2)-fractional Laplacian. The main result generalizes the corresponding LDP result of the classical stochastic 3D Leray-alpha model (theta(1) = 1, theta(2) = 1), and it is also applicable to the stochastic 3D hyperviscous Navier-Stokes equations (theta(1) = 0, theta(2) >= 5/4) and stochastic 3D critical Leray-alpha model (theta(1) = 1/4, theta(2) = 1).