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Journal of Applied Mathematics and Stochastic Analysis
Volume 13, Issue 3, Pages 239-259
http://dx.doi.org/10.1155/S1048953300000228

Galerkin approximation and the strong solution of the Navier-Stokes equation

Martin-Luther Universität Halle- Wittenberg, Fachbereich Mathematik und Informatik, Institut für Optimierung und Stochastik, Halle (Saale) D-06099, Germany

Received 1 June 1998; Revised 1 June 1999

Copyright © 2000 Hindawi Publishing Corporation. 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 consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.