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Open Access Research Article

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

Gabriel Deugoue12 and Mamadou Sango1*

Author Affiliations

1 Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa

2 Department of Mathematics and Computer Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon

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Boundary Value Problems 2010, 2010:723018  doi:10.1155/2010/723018

Published: 2 February 2010

Abstract

We prove the existence and uniqueness of strong solution to the stochastic Leray- 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.