On the Rate of Convergence of the 2-D Stochastic Leray- α Model to the 2-D Stochastic Navier–Stokes Equations with Multiplicative Noise
Article
Bessaih, H, Razafimandimby, PA. (2016). On the Rate of Convergence of the 2-D Stochastic Leray- α Model to the 2-D Stochastic Navier–Stokes Equations with Multiplicative Noise
. APPLIED MATHEMATICS AND OPTIMIZATION, 74(1), 1-25. 10.1007/s00245-015-9303-7
Bessaih, H, Razafimandimby, PA. (2016). On the Rate of Convergence of the 2-D Stochastic Leray- α Model to the 2-D Stochastic Navier–Stokes Equations with Multiplicative Noise
. APPLIED MATHEMATICS AND OPTIMIZATION, 74(1), 1-25. 10.1007/s00245-015-9303-7
In the present paper we study the convergence of the solution of the two dimensional (2-D) stochastic Leray-α model to the solution of the 2-D stochastic Navier–Stokes equations. We are mainly interested in the rate, as α→ 0 , of the following error function (Formula presented.) and u are the solution of stochastic Leray-α model and the stochastic Navier–Stokes equations, respectively. We show that when properly localized the error function εα converges in mean square as α→ 0 and the convergence is of order O(α). We also prove that εα converges in probability to zero with order at most O(α).
