Boundary Value Problems
Volume 2010 (2010), Article ID 723018, 31 pages
doi:10.1155/2010/723018
Research Article

On the Strong Solution for the 3D Stochastic Leray-Alpha Model

Gabriel Deugoue1,2 and Mamadou Sango1

1Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa
2Department of Mathematics and Computer Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon

Received 13 August 2009; Accepted 27 January 2010

Academic Editor: Vicentiu D. Radulescu

Copyright © 2010 Gabriel Deugoue and Mamadou Sango. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove the existence and uniqueness of strong solution to the stochastic Leray-α equations under appropriate conditions on the data. This is achieved by means of the Galerkin approximation scheme. We also study the asymptotic behaviour of the strong solution as alpha goes to zero. We show that a sequence of strong solutions converges in appropriate topologies to weak solutions of the 3D stochastic Navier-Stokes equations.