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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


The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2010/1/723018


Received:13 August 2009
Accepted:27 January 2010
Published:2 February 2010

© 2010 The Author(s).

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- 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.

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