Averaging principle for stochastic 3D fractional Leray-α model with a fast oscillation. Issue 2 (3rd March 2020)

• Record Type: Journal Article
• Authors: Li, Shihu; Xie, Yingchao
• Is Part Of: Stochastic analysis and applications. Volume 38:Issue 2(2020)
• Page Start: 248
• Page End: 276
• Publication Date: 2020-03-03
• Subjects: Stochastic Leray-α model -- averaging principle -- multi-scaling limit -- strong convergence -- fractional Laplacian; 60H15 -- 35Q10 -- 70K70; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2019.1689141
• Languages: English
• ISSNs: 0736-2994

Abstract

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 ).