Averaging principle for stochastic 3D fractional Leray-α model with a fast oscillation. Issue 2 (3rd March 2020) - Li, Shihu; Xie, Yingchao
Abstract: This article investigates the multiscale stochastic 3D fractional Leray-α model. By using the Khasminskii technique, we establish the strong average principle for stochastic 3D fractional Leray-α model with a fast oscillation. This model is the stochastic 3D Navier–Stokes equations regularized through a smoothing kernel of order θ1 in the nonlinear term and a θ2 -fractional Laplacian. The main result is applicable to the classical stochastic 3D Leray-α model ( θ 1 = 1, θ 2 = 1 ), stochastic 3D hyperviscous Navier–Stokes equations ( θ 1 = 0, θ 2 ≥ 5 4 ) and stochastic 3D critical Leray-α model ( θ 1 = 1 4, θ 2 = 1 ).