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 (), stochastic 3D hyperviscous Navier–Stokes equations (
) and stochastic 3D critical Leray-α model (
).
Acknowledgment
The authors would like to thank the referee for his/her very valuable suggestions and useful remarks which helped to considerably improve the quality of the article.